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There is a list with 17 elements a={0.026284, 0.057253, 0.124713, 0.271658, 0.591744, 1.288974, 2.807725, 6.115966, 13.322188, 29.019243, 63.211573, 137.691494, 299.928425, 653.323290, 1423.110603, 3099.910594, 6752.423650}

The elements in the list are written according to a certain rule that I don't know. I would like to expand this list in both directions like here anew={... a, b, c, 0.026284, 0.057253, 0.124713, 0.271658, 0.591744, 1.288974, 2.807725, 6.115966, 13.322188, 29.019243, 63.211573, 137.691494, 299.928425, 653.323290, 1423.110603, 3099.910594, 6752.423650, d, e, f ...} where ...a, b, c and d, e, f... are elements which fit the general rule.

How to find this rule and write down additional elements (or just find the most suitable elements)?

All elements should be a positive

ClearAll["Global`*"]
a={0.026284, 0.057253, 0.124713, 0.271658, 0.591744, 1.288974, 2.807725,6.115966, 13.322188, 29.019243, 63.211573, 137.691494, 299.928425,653.323290, 1423.110603, 3099.910594, 6752.423650};

There is a list with 19 elements a={0.500074`, 0.502676`, 0.510451`, 0.507502`, 0.52768`, 0.625164`, 0.935248`, 1.826161`, 3.845598`, 8.293859`, 18.014295`, 39.20736`, 85.3836`, 185.975252`, 405.095196`, 882.399269`, 1922.095421`, 4186.829292`, 9120.018288`}

The elements in the list are written according to a certain rule that I don't know. I would like to expand this list in both directions like here anew={... a, b, c, 0.500074`, 0.502676`, 0.510451`, 0.507502`, 0.52768`, 0.625164`, 0.935248`, 1.826161`, 3.845598`, 8.293859`, 18.014295`, 39.20736`, 85.3836`, 185.975252`, 405.095196`, 882.399269`, 1922.095421`, 4186.829292`, 9120.018288`, d, e, f ...} where ...a, b, c and d, e, f... are elements which fit the general rule.

How to find this rule and write down additional elements (or just find the most suitable elements)?

All elements should be a positive

ClearAll["Global`*"]
a={0.500074`, 0.502676`, 0.510451`, 0.507502`, 0.52768`, 0.625164`,    0.935248`, 1.826161`, 3.845598`, 8.293859`, 18.014295`, 39.20736`,    85.3836`, 185.975252`, 405.095196`, 882.399269`, 1922.095421`,    4186.829292`, 9120.018288`};

There is a list with 17 elements a={0.026284, 0.057253, 0.124713, 0.271658, 0.591744, 1.288974, 2.807725, 6.115966, 13.322188, 29.019243, 63.211573, 137.691494, 299.928425, 653.323290, 1423.110603, 3099.910594, 6752.423650}

The elements in the list are written according to a certain rule that I don't know. I would like to expand this list in both directions like here anew={... a, b, c, 0.026284, 0.057253, 0.124713, 0.271658, 0.591744, 1.288974, 2.807725, 6.115966, 13.322188, 29.019243, 63.211573, 137.691494, 299.928425, 653.323290, 1423.110603, 3099.910594, 6752.423650, d, e, f ...} where ...a, b, c and d, e, f... are elements which fit the general rule.

How to find this rule and write down additional elements (or just find the most suitable elements)?

All elements should be a positive

There is a list with 17 elements a={0.026284, 0.057253, 0.124713, 0.271658, 0.591744, 1.288974, 2.807725, 6.115966, 13.322188, 29.019243, 63.211573, 137.691494, 299.928425, 653.323290, 1423.110603, 3099.910594, 6752.423650}

The elements in the list are written according to a certain rule that I don't know. I would like to expand this list in both directions like here anew={... a, b, c, 0.026284, 0.057253, 0.124713, 0.271658, 0.591744, 1.288974, 2.807725, 6.115966, 13.322188, 29.019243, 63.211573, 137.691494, 299.928425, 653.323290, 1423.110603, 3099.910594, 6752.423650, d, e, f ...} where ...a, b, c and d, e, f... are elements which fit the general rule.

How to find this rule and write down additional elements (or just find the most suitable elements)?

All elements should be a positive

ClearAll["Global`*"]
a={0.026284, 0.057253, 0.124713, 0.271658, 0.591744, 1.288974, 2.807725,6.115966, 13.322188, 29.019243, 63.211573, 137.691494, 299.928425,653.323290, 1423.110603, 3099.910594, 6752.423650};

There is a list with 17 elements a={0.026284, 0.057253, 0.124713, 0.271658, 0.591744, 1.288974, 2.807725, 6.115966, 13.322188, 29.019243, 63.211573, 137.691494, 299.928425, 653.323290, 1423.110603, 3099.910594, 6752.423650}

The elements in the list are written according to a certain rule that I don't know. I would like to expand this list in both directions like here anew={... a, b, c, 0.026284, 0.057253, 0.124713, 0.271658, 0.591744, 1.288974, 2.807725, 6.115966, 13.322188, 29.019243, 63.211573, 137.691494, 299.928425, 653.323290, 1423.110603, 3099.910594, 6752.423650, d, e, f ...} where ...a, b, c and d, e, f... are elements which fit the general rule.

How to find this rule and write down additional elements (or just find the most suitable elements)?

All elements have to be a positive

There is a list with 17 elements a={0.026284, 0.057253, 0.124713, 0.271658, 0.591744, 1.288974, 2.807725, 6.115966, 13.322188, 29.019243, 63.211573, 137.691494, 299.928425, 653.323290, 1423.110603, 3099.910594, 6752.423650}

The elements in the list are written according to a certain rule that I don't know. I would like to expand this list in both directions like here anew={... a, b, c, 0.026284, 0.057253, 0.124713, 0.271658, 0.591744, 1.288974, 2.807725, 6.115966, 13.322188, 29.019243, 63.211573, 137.691494, 299.928425, 653.323290, 1423.110603, 3099.910594, 6752.423650, d, e, f ...} where ...a, b, c and d, e, f... are elements which fit the general rule.

How to find this rule and write down additional elements (or just find the most suitable elements)?

All elements should be a positive