A178237 Smallest prime p of the form prime(n)+k^2 such that sum of digits(p) = prime(n).

2, 3, 5, 7, 47, 157, 593, 919, 599, 66593, 46687, 396937, 467897, 467899, 6969647, 16499897, 367488959, 598095997, 2977884967, 4977866987, 2797986889, 58888728979, 58987779959, 679585896989, 4989996468997

Offset

1,1

Comments

It is still an open problem if there exist infinitely many primes of form k^2 + d (d integer, no negative square).

For n<=4, k=0 suffices: e.g. prime(1)+0^2=2 = sum of digits(prime(1)), so a(n)=prime(n).

Links

Table of n, a(n) for n=1..25.

Example

a(13) = 467897 because its digitsum is 41 which is the 13th prime, it is of the form prime(13)+k^2 with k=684, and it is the least such prime.

Prog

(PARI) sod(n) = {digs = digits(n, 10); return (sum(j=1, #digs, digs[j])); }
a(n) = {k = 0; p = prime(n); while (! (isprime(q=p+k^2) && (sod(q) == p)), k++); return (q); } \\ Michel Marcus, Jul 26 2013

Crossrefs

Cf. A000040, A172035, A176111, A176790

Sequence in context: A052016 A171020 A214179 * A118842 A364831 A244595

Adjacent sequences: A178234 A178235 A178236 * A178238 A178239 A178240

Keyword

base,nonn

Author

Ulrich Krug (leuchtfeuer37(AT)gmx.de), May 23 2010

Extensions

a(5) corrected and sequence extended by D. S. McNeil, May 25 2010

Status

approved