A227785 Primes p such that p - ssd(p) is the square of a prime, where ssd(k) is the sum of the squared decimal digits of k.

11, 2903, 3533, 3803, 5197, 9533, 18973, 24763, 37321, 73561, 96953, 113621, 124777, 129097, 134837, 139241, 398341, 830003, 1100509, 1585201, 1661789, 2211257, 4541309, 4871077, 4897709, 5340949, 5958751, 7393123, 8185501, 8744003, 11485559, 15343039, 15343079

Offset: 1

Author

Underwood Dudley, Will Gosnell, Charles R Greathouse IV, and Robert Israel, Aug 09 2013

Keywords

• nonn
• base

Examples

			11 is a member since 11 - 2 = 3^2 where 3 is prime. 2903 is a member since 2903 - 94 = 53^2 where 53 is prime.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..2900

Crossrefs

Subsequence of A119449. ssd(n) = A003132(n).

Programs

Maple

ssd:= n->add(d^2,d=convert(n,base,10));
S:= select(t -> type(sqrt(t - ssd(t)),prime), [seq(ithprime(j),j=1..10^5)]);

Mathematica

fQ[n_] := PrimeQ[ Sqrt[ n - Total[ IntegerDigits[ n]^2]]]; p = 2; lst = {}; While[p < 15500000, If[ fQ@ p, AppendTo[ lst, p]]; p = NextPrime@ p]; lst (* Robert G. Wilson v, Jun 01 2014 *)

PARI

ssd(n)=my(d=digits(n));sum(i=1,#d,d[i]^2)
v=List();forprime(p=2,1e5,if(issquare(p-ssd(p),&t) && isprime(t), listput(v,p))); Vec(v)