A256917 Primes which are not the sums of two consecutive nonsquares.

2, 3, 7, 17, 19, 31, 71, 73, 97, 127, 163, 199, 241, 337, 449, 577, 647, 881, 883, 967, 1151, 1153, 1249, 1459, 1567, 1801, 2179, 2311, 2591, 2593, 2887, 3041, 3361, 3527, 3529, 3697, 4049, 4051, 4231, 4801, 4999, 5407, 6271, 6961, 7687, 7937, 8191, 8713, 9521, 10369, 10657

Offset: 1

Author

Juri-Stepan Gerasimov, Apr 23 2015

Keywords

• nonn
• easy

Comments

The union of 2 and A066436 and A090698.

The sums of two consecutive nonsquares are 5, 8, 11, 13, 15, 18, 21, 23, 25, 27, 29, 32, 35, 37, ...

Examples

			2, 3, 7 are in this sequence because first three sums of two consecutive nonsquares are 5, 8, 11 and 2, 3, 7 are primes.
		

Links

• Colin Barker and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 800 terms from Barker)

Crossrefs

Cf. A000037, A066436, A090698, A154670.

Programs

Mathematica

Union[{2},Select[Table[2n^2-1,{n,0,1000}],PrimeQ],Select[Table[2n^2+1,{n,0,1000}],PrimeQ]] (* Ivan N. Ianakiev, Apr 24 2015 *)
Module[{nn=11000,ns},ns=Total/@Partition[Select[Range[nn],!IntegerQ[Sqrt[#]]&],2,1]; Complement[ Prime[Range[PrimePi[Last[ns]]]],ns]] (* Harvey P. Dale, Mar 06 2024 *)

PARI

a256917(maxp) = {
  ps=[2];
  k=1; while((t=2*k^2-1)<=maxp, k++; if(isprime(t), ps=setunion(ps, [t])));
  k=1; while((t=2*k^2+1)<=maxp, k++; if(isprime(t), ps=setunion(ps, [t])));
  ps
}
a256917(11000) \\ Colin Barker, Apr 23 2015

PARI

list(lim)=my(v=List([2]),t); for(k=2,sqrtint((lim+1)\2), if(isprime(t=2*k^2-1), listput(v,t))); for(k=1,sqrtint((lim-1)\2), if(isprime(t=2*k^2+1), listput(v,t))); Set(v) \\ Charles R Greathouse IV, Apr 23 2015