A165502 Primes p where the digital sum of p^2 is equal to 31.

83, 137, 173, 223, 263, 277, 281, 367, 443, 457, 547, 587, 673, 677, 691, 727, 853, 857, 907, 911, 997, 1033, 1087, 1109, 1163, 1181, 1213, 1217, 1307, 1433, 1447, 1523, 1613, 1627, 1699, 1721, 1811, 2027, 2153, 2203, 2221, 2297, 2347, 2459, 2473, 2477, 2531, 2549

Offset: 1

Author

Vincenzo Librandi, Sep 21 2009

Keywords

• nonn
• base

Examples

			83 is in the sequence because 83^2=6889 and 6+8+8+9=31.
1721 is in the sequence because 1721^2=2961841 and 2+9+6+1+8+4+1=31.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Programs

Magma

[p: p in PrimesUpTo(2600) | &+Intseq(p^2) eq 31]; // Vincenzo Librandi, Sep 12 2013

Maple

A007953 := proc(n) add(d,d=convert(n,base,10)) ; end:
A123157 := proc(n) A007953((ithprime(n))^2) ; end:
for n from 1 to 10000 do if A123157(n) = 31 then printf("%d,",ithprime(n)) ; fi; od: # R. J. Mathar, Sep 29 2009

Mathematica

Select[Prime[Range[500]], Total[IntegerDigits[#^2]]== 31 &]  (* Harvey P. Dale, Apr 13 2011 *)

Formula

{A000040(i) : A123157(i) = 31} [R. J. Mathar, Sep 29 2009]

Extensions

Edited by R. J. Mathar, Sep 29 2009