A227994 - OEIS

%I #36 Jun 10 2021 11:15:01

%S 461,773,1181,1973,2621,6173,7901,9173,11261,21773,29501,37061,44021,

%T 50021,51581,54773,58061,66701,68501,72173,75941,81773,85781,96221,

%U 109541,118901,126173,143981,204461,210773,220421,233621,236981,254141,279173,286541,328781,336773

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

%C Primes of the form 3k^2 + 42k + 245. - _Charles R Greathouse IV_, Aug 14 2013

%H Harvey P. Dale, <a href="/A227994/b227994.txt">Table of n, a(n) for n = 1..1000</a>

%e 461 is a term since 4^2 + 11^2 + 18^2 = 461;

%e 773 is a term since 8^2 + 15^2 + 22^2 = 773;

%e 1181 is a term since 12^2 + 19^2 + 26^2 = 1181;

%e 1973 is a term since 18^2 + 25^2 + 32^2 = 1973.

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

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

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

%Y Subsequence of A085317. - _Michel Marcus_, Apr 01 2019

%K nonn

%O 1,1

%A _Will Gosnell_, Aug 14 2013

%E a(14)-a(38) from _Charles R Greathouse IV_, Aug 14 2013

%E Name clarified by _Jon E. Schoenfield_, Apr 01 2019