A270971 First differences of (provable) Sierpiński numbers (A076336).

192572, 448, 50946, 5216, 154980, 92322, 28672, 300270, 30926, 30522, 294348, 30898, 228104, 105316, 15362, 138154, 353430, 56, 60432, 318646, 31424, 34488, 355678, 224, 151732, 14336, 457534, 52658, 458752, 28856, 478140, 881790, 386158, 292716, 896, 422284, 119078, 1792, 63774

Offset

1,1

Comments

If we analyze the b-file of A076336, we see that most repeated values of a(n) are the form of 14*(2^k), for k >= 0. For the first 15000 (provable) Sierpiński numbers, there are 200 times 14, 201 times 28, 200 times 56, 200 times 112, 201 times 224, 200 times 448, 199 times 896, 200 times 1792, 200 times 3584 in this sequence.

Additionally, 14 appears as a minimum difference between consecutive (provable) Sierpiński numbers for the first 15000 terms that are listed in b-file of A076336. Graph of the sequence that is integers n such that A076336(n+1) = A076336(n) + 14 seems approximately linear.

The minimum value of this sequence is 2, as the numbers 3913004084027, 3913004084029 are consecutive odd numbers that are both Sierpinski numbers. - Robert Gelhar, Jul 23 2020

Links

Table of n, a(n) for n=1..39.

Formula

a(n) = A076336(n+1) - A076336(n).

Example

a(1) = A076336(2) - A076336(1) = 271129 - 78557 = 192572.

Crossrefs

Cf. A076336.

Sequence in context: A254427 A253373 A204228 * A234455 A187676 A187674

Adjacent sequences: A270968 A270969 A270970 * A270972 A270973 A270974

Keyword

nonn

Author

Altug Alkan, Mar 27 2016

Status

approved