A165493 Primes p where the digital sum of p^2 is equal to 19.

17, 37, 53, 73, 89, 107, 109, 127, 181, 199, 269, 271, 379, 503, 521, 557, 701, 739, 1009, 1061, 1097, 1151, 1171, 1439, 1511, 1601, 1619, 1747, 1801, 1871, 2251, 3169, 3259, 3329, 3347, 3511, 3761, 3851, 3889, 4051, 4139, 4519, 4751, 4951, 5003, 5021, 5849

Offset: 1

Author

Vincenzo Librandi, Sep 21 2009

Keywords

• nonn
• base

Examples

			17 is in the sequence because 17^2=289 and 2+8+9=19.
1801 is in the sequence because 1801^2=3243601 and 3+2+4+3+6+0+1=19.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..215

Programs

Magma

[p: p in PrimesUpTo(6000) | &+Intseq(p^2) eq 19]; // Bruno Berselli, Jun 24 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 100000 do if A123157(n) = 19 then printf("%d,",ithprime(n)) ; fi; od: # R. J. Mathar, Sep 29 2009

Mathematica

Select[Prime[Range[800]], Total[IntegerDigits[#^2]]== 19&] (* Vincenzo Librandi, Jun 24 2013 *)

Formula

{A000040(i) : A123157(i) = 19} [R. J. Mathar, Sep 29 2009]

Extensions

More terms from R. J. Mathar, Sep 29 2009