A227994 Primes that are the sum of the squares of three integers that form an arithmetic sequence with difference 7.

461, 773, 1181, 1973, 2621, 6173, 7901, 9173, 11261, 21773, 29501, 37061, 44021, 50021, 51581, 54773, 58061, 66701, 68501, 72173, 75941, 81773, 85781, 96221, 109541, 118901, 126173, 143981, 204461, 210773, 220421, 233621, 236981, 254141, 279173, 286541, 328781, 336773

Offset

1,1

Comments

Primes of the form 3k^2 + 42k + 245. - Charles R Greathouse IV, Aug 14 2013

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

461 is a term since 4^2 + 11^2 + 18^2 = 461;
773 is a term since 8^2 + 15^2 + 22^2 = 773;
1181 is a term since 12^2 + 19^2 + 26^2 = 1181;
1973 is a term since 18^2 + 25^2 + 32^2 = 1973.

Maple

for x in range(1, 2000): b=x**2  : c= (x+7)**2: d=(x+14)**2:e=(b+c+d): print x, e

Mathematica

Select[Table[Total[(n+{0, 7, 14})^2], {n, 500}], PrimeQ] (* Harvey P. Dale, Jun 10 2021 *)

Prog

(PARI) for(n=1, 1e3, if(isprime(t=3*(n+7)^2+98), print1(t", "))) \\ Charles R Greathouse IV, Aug 14 2013

Crossrefs

Subsequence of A085317. - Michel Marcus, Apr 01 2019

Sequence in context: A264242 A358894 A107973 * A142832 A277989 A138956

Adjacent sequences: A227991 A227992 A227993 * A227995 A227996 A227997

Keyword

nonn

Author

Will Gosnell, Aug 14 2013

Extensions

a(14)-a(38) from Charles R Greathouse IV, Aug 14 2013

Name clarified by Jon E. Schoenfield, Apr 01 2019

Status

approved