A126142 Primes p such that the sum of the decimal digits of p^2 is also a prime.

5, 7, 17, 29, 37, 47, 53, 61, 73, 79, 83, 89, 107, 109, 127, 137, 149, 151, 173, 181, 199, 223, 263, 269, 271, 277, 281, 349, 367, 379, 389, 433, 443, 457, 461, 503, 521, 547, 557, 587, 601, 613, 673, 677, 683, 691, 701, 727, 739, 773, 827, 853, 857, 863, 887

Offset

1,1

Comments

a(n)^2 is of the form 6*k+1. [Vincenzo Librandi, Sep 21 2009; edited by Klaus Brockhaus, Nov 23 2009; edited by Bruno Berselli, Jun 06 2014]

This comment is trivially true: after 3, the square of each prime has the form 6*k+1. [Bruno Berselli, Jun 06 2014]

Links

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

Example

5^2=25, 2+5=7.
7^2=49, 4+9=13.
17^2=289, 2+8+9=19.

Maple

P:=proc(n) local i, k, w; for i from 1 by 1 to n do w:=0; k:=ithprime(i)^2; while k>0 do w:=w+(k-trunc(k/10)*10); k:=trunc(k/10); od; if isprime(w) then print(ithprime(i), w); fi; od; end: P(1000);

Mathematica

Select[Prime[Range[1000]], PrimeQ[Apply[Plus, IntegerDigits[#^2]]] &] (* Vincenzo Librandi, Jun 06 2014 *)

Prog

(Magma) [p: p in PrimesUpTo(1000) | IsPrime(&+Intseq(p^2))]; // Klaus Brockhaus, Nov 23 2010

Crossrefs

Sequence in context: A032412 A114970 A048710 * A216560 A019340 A290471

Adjacent sequences: A126139 A126140 A126141 * A126143 A126144 A126145

Keyword

nonn,base,easy

Author

Paolo P. Lava and Giorgio Balzarotti, Mar 07 2007

Extensions

Definition reworded by Klaus Brockhaus, Nov 23 2010

Status

approved