A230087 Primes such that prime plus its digit sum is a perfect square.

2, 17, 179, 347, 467, 521, 1433, 1583, 2111, 3347, 10601, 12527, 25889, 28541, 32027, 33113, 39569, 39971, 41201, 43661, 45767, 55667, 58061, 59513, 61001, 62969, 63977, 67061, 70199, 77261, 92387, 92993, 100469, 109541, 120401, 122477, 130307, 156011, 163193

Offset: 1

Author

K. D. Bajpai, Oct 08 2013

Keywords

• nonn
• base
• less

Comments

Number of primes obtained from the sequence ‘prime plus its digit sum is perfect square’ is 150 for n = 1 to 3*10^5, while the sequence for ‘perfect cube’ yields only 11 primes for the same range of n. Hence, sequence for ‘square’ is framed.

Subsequence of primes of A066564. - Michel Marcus, Jun 02 2015

Examples

			a(2) = 17 is prime. Digit sum of 17 = 8, 17 + 8 = 25 = 5^2.
a(5) = 467 is prime. Digit sum of 467 = 17, 467 + 17 = 484 = 22^2.
		

Links

• K. D. Bajpai and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (terms 2..150 from Bajpai)

Crossrefs

Cf. A048519.

Cf. A107288 (Primes whose digit sum is square).

Programs

Magma

[p: p in PrimesUpTo(6*10^5) | IsSquare(p+(&+Intseq(p)))]; // Vincenzo Librandi, Jun 02 2015

Maple

KD:= proc() local a,b,c,d; a:= ithprime(n);b:=add( i,i = convert((a), base, 10))(a); c:=a+b; d:=evalf(sqrt(c)); if d=floor(d) then return (a) :fi;end:seq(KD(),n=1..50000);

PARI

for(n=2,1e4,forprime(p=n^2-9*#digits(n^2),n^2, if(p+sumdigits(p) == n^2, print1(p", ")))) \\ Charles R Greathouse IV, Oct 08 2013

Extensions

a(1) from Charles R Greathouse IV, Oct 08 2013