A165459 Primes p such that the sum of the digits of p^2 is 16.

13, 23, 31, 41, 59, 103, 131, 139, 211, 229, 239, 347, 401, 491, 499, 571, 751, 1021, 1201, 1229, 1453, 1489, 1499, 1741, 2003, 2011, 3001, 3821, 4001, 4639, 4649, 5701, 7079, 8951, 10111, 10247, 10301, 10499, 14251, 14639, 16249, 17321, 19751, 20011

Offset: 1

Author

Vincenzo Librandi, Sep 20 2009

Keywords

• nonn
• less
• base

Examples

			31 is in the sequence because 31^2=961 and 9+6+1=16;
1489 is in the sequence because 1489^2=2217121 and 2+2+1+7+1+2+1=16;
3001 is in the sequence because 3001^2=9006001 and 9+0+0+6+0+0+1=16.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..80

Programs

Magma

[p: p in PrimesUpTo(3*10^4) | &+Intseq(p^2) eq 16]; // Bruno Berselli, Jun 24 2013

Maple

A007953 := proc(n) local d ; add(d, d=convert(n,base,10)) ; end proc: A165459 := proc(n) local a ; if n = 1 then 13; else a := nextprime( procname(n-1)) ; while A007953(a^2) <> 16 do a := nextprime(a) ; end do ; return a ; end if; end proc: seq(A165459(n),n=1..50) ; # R. J. Mathar, Nov 09 2009

Mathematica

Select[Prime[Range[3000]], Total[IntegerDigits[#^2]]==16 &] (* Vincenzo Librandi, Jun 24 2013 *)

Formula

{A000040(i) : A123157(i) = 16}. [R. J. Mathar, Nov 09 2009]

Extensions

Edited by N. J. A. Sloane, Sep 25 2009

347 inserted, more terms added by R. J. Mathar, Nov 09 2009