A042939 -id:A042939 - cp's OEIS frontend

A115261 Prime numbers such that the absolute difference of the sum of their digits in odd positions and the sum of their digits in even positions is also a prime.

2, 3, 5, 7, 13, 29, 31, 41, 47, 53, 61, 79, 83, 97, 101, 113, 137, 139, 151, 157, 163, 167, 173, 179, 191, 193, 211, 223, 227, 233, 251, 269, 277, 281, 283, 311, 313, 337, 359, 379, 383, 401, 409, 421, 431, 443, 467, 487, 541, 557, 563, 577, 599, 601, 607, 641

Offset: 1

Paolo P. Lava and Giorgio Balzarotti, Jan 20 2006

			1237 is in the sequence because it is prime and abs((7+2)-(3+1)) = 5 is prime

Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Cf. A040997, A005017, A063792, A087593, A042939, A041000, A040164, A115259, A115260.

Df:=proc(N) j:=1; for n from 1 while j<=N do B:= convert(ithprime(n),base,10); ap:=-(sum(B[2*i],i=1..nops(B)/2)-sum(B[2*n+1],i=0..(nops(B)-1)/2)); if (isprime(abs(ap)) = true) then a[j]:=ithprime(n); j:=j+1; fi; od; end:

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

Original entry on oeis.org

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

Giorgio Balzarotti and Paolo P. Lava, Jan 20 2006

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

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

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

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

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

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 *)

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

A115260 Prime numbers in the sequence of the absolute difference of the sum of digits in odd positions and the sum of digits in even positions of prime numbers.

Original entry on oeis.org

2, 3, 5, 7, 2, 7, 2, 3, 3, 2, 5, 2, 5, 2, 2, 3, 5, 7, 3, 3, 2, 2, 3, 3, 7, 5, 2, 3, 7, 2, 2, 5, 2, 5, 3, 3, 5, 7, 7, 5, 2, 5, 13, 3, 2, 3, 5, 3, 2, 7, 2, 5, 5, 7, 13, 3, 5, 2, 2, 7, 13, 3, 2, 3, 5, 17, 7, 13, 5, 3, 7, 17, 13, 7, 3, 7, 7, 2, 3, 5, 5, 2, 2, 7, 3, 3, 7, 2, 3, 7, 2, 3, 7, 2, 5, 5, 3, 2, 7, 3, 5, 7

Offset: 1

Giorgio Balzarotti, Paolo P. Lava, Jan 20 2006

Primes in the sequence A115259.

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

Cf. A040997, A005017, A063792, A087593, A042939, A041000, A040164, A115259, A115261.

select(isprime,[seq(abs(sum(convert(ithprime(a),base,10)[2*i],i=1..nops(convert (ithprime(a),base,10))/2)-sum(convert(ithprime(a),base,10)[2*i+1],i=0..(nops (convert(ithprime(a),base,10))-1)/2)),a=1..N)]);

A185107 a(n) is the first digit of prime(n) minus the sum of the other digits.

Original entry on oeis.org

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, 0, -2, -6, -8, -3, -8, -3, -9, -11, -12, -5, -11, -8, -12, -9, -15, -8, -9, -11, -15, -17, 0, -3, -7, -9, -4, -10, -3, -4, -10, -7, -13

Offset: 1

Dario Piazzalunga, Dec 27 2012

Absolute terms are the same as A042939.

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

Cf. A000040, A042939, A007605.

Table[With[{id=IntegerDigits[Prime[n]]},id[[1]]-Total[Rest[id]]],{n,60}] (* Harvey P. Dale, Oct 04 2024 *)

a(n) = {digs = digits(prime(n)); digs[1] - sum(i=2, #digs, digs[i]);} \\ Michel Marcus, Aug 30 2013

a(38) corrected by Michel Marcus, Jun 14 2022

cp's OEIS Frontend

A115261 Prime numbers such that the absolute difference of the sum of their digits in odd positions and the sum of their digits in even positions is also a prime.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Formula

A115260 Prime numbers in the sequence of the absolute difference of the sum of digits in odd positions and the sum of digits in even positions of prime numbers.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Maple

A185107 a(n) is the first digit of prime(n) minus the sum of the other digits.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Extensions