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

1,1

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, ...

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A000037, A066436, A090698, A154670.

Sequence in context: A160513 A154431 A350118 * A089144 A171430 A355419

Adjacent sequences: A256914 A256915 A256916 * A256918 A256919 A256920

Keyword

nonn,easy

Author

Juri-Stepan Gerasimov, Apr 23 2015

Status

approved