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

Author

Giorgio Balzarotti and Paolo P. Lava, Jan 20 2006

Keywords

• base
• sign

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

Examples

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

Links

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

Crossrefs

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

Programs

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 *)

Formula

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