A115259 Difference between the sum of digits in odd positions and the sum of digits in even positions of prime numbers.

2, 3, 5, 7, 0, 2, 6, 8, 1, 7, -2, 4, -3, -1, 3, -2, 4, -5, 1, -6, -4, 2, -5, 1, -2, 2, 4, 8, 10, 3, 6, -1, 5, 7, 6, -3, 3, -2, 2, -3, 3, -6, -7, -5, -1, 1, 2, 3, 7, 9, 2, 8, -1, -2, 4, -1, 5, -4, 2, -5, -3, -4, 10, 3, 5, 9, 1, 7, 6, 8, 1, 7, 4, -1, 5, -2, 4, 1, 5, 13, 12, 3, 2, 4, 10, 3, 9, 6, -1, 1, 5, 6, 3, -4, 4, 8, 14, 4, 6, 2, 8, 7, 2, 8, -1, 5, 4, -1, 5, 7

Offset

1,1

Comments

Zero corresponds to the prime 11. It is easy to show that there is no other zero: if the difference of odd-even digits of a number is zero, the number is a multiple of 11, i.e., it is not a prime.

Positions are counted from the least to the most significant digit, so for prime 17 the odd digit is 7 and the even digit is 1. - Harvey P. Dale, Dec 15 2022

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

a(n) = A055017(A000040(n)). - R. J. Mathar, Aug 26 2011

Example

a(37) = 3 because 37th prime = 157, (7+1) - 5 = 3.

Maple

A115259 := proc(n) A055017(ithprime(n)) ; end proc: # R. J. Mathar, Aug 26 2011

Mathematica

Table[Total[Take[Reverse[IntegerDigits[p]], {1, -1, 2}]]-Total[Take[Reverse[IntegerDigits[p]], {2, -1, 2}]], {p, Prime[Range[120]]}] (* Harvey P. Dale, Dec 15 2022 *)

Crossrefs

Cf. A040997, A055017, A063792, A087593, A042939, A041000, A040164, A115260, A115261.

Sequence in context: A041000 A185107 A042939 * A039709 A346512 A104250

Adjacent sequences: A115256 A115257 A115258 * A115260 A115261 A115262

Keyword

base,sign

Author

Giorgio Balzarotti and Paolo P. Lava, Jan 20 2006

Status

approved