A154275 Primes p=prime(k) such that abs(sum of digits of p - sum of digits of k) is prime.

5, 7, 11, 13, 19, 31, 37, 43, 47, 61, 67, 73, 89, 103, 107, 113, 137, 151, 157, 167, 173, 193, 211, 223, 227, 233, 239, 269, 271, 277, 281, 311, 353, 373, 379, 401, 409, 419, 421, 431, 433, 439, 443, 449, 467, 487, 503, 509, 571, 599, 601, 631, 641, 647, 653

Offset: 1

Author

Juri-Stepan Gerasimov, Jan 06 2009

Keywords

• nonn
• base
• less

Examples

			Prime(36)=151 and abs(1+5+1-(3+6)) = abs(7-9) = 2 (a prime), so 151 is in the sequence.
Prime(37)=157 and abs(1+5+7-(3+7)) = abs(13-10) = 3 (a prime), so 157 is in the sequence.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A000040.

Programs

Maple

A007953 := proc(n) add(i,i=convert(n,base,10)) ; end: A007605 := proc(n) A007953(ithprime(n)) ; end: A090431 := proc(n) A007953(n)-A007605(n) ; end: for n from 1 to 200 do q := abs(A090431(n)) ; if isprime(q) then p := ithprime(n) ; printf("%a,",p) ; fi; od: # R. J. Mathar, Jan 07 2009

Mathematica

Transpose[Select[Table[{n,Prime[n]},{n,200}],PrimeQ[Abs[Total[ IntegerDigits[ #[[2]]]] -Total[IntegerDigits[#[[1]]]]]]&]][[2]] (* Harvey P. Dale, Jan 27 2013 *)

Extensions

103, 113 etc. inserted by R. J. Mathar, Jan 07 2009

Name edited by Jon E. Schoenfield, Jan 06 2019