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

1,1

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

Links

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

Example

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.

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);

Prog

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

Crossrefs

Cf. A048519.

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

Sequence in context: A011550 A102023 A212833 * A058010 A242428 A199751

Adjacent sequences: A230084 A230085 A230086 * A230088 A230089 A230090

Keyword

nonn,base,less

Author

K. D. Bajpai, Oct 08 2013

Extensions

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

Status

approved