cp's OEIS Frontend

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

%I A256917 #37 Mar 06 2024 11:18:23
%S A256917 2,3,7,17,19,31,71,73,97,127,163,199,241,337,449,577,647,881,883,967,
%T A256917 1151,1153,1249,1459,1567,1801,2179,2311,2591,2593,2887,3041,3361,
%U A256917 3527,3529,3697,4049,4051,4231,4801,4999,5407,6271,6961,7687,7937,8191,8713,9521,10369,10657
%N A256917 Primes which are not the sums of two consecutive nonsquares.
%C A256917 The union of 2 and A066436 and A090698.
%C A256917 The sums of two consecutive nonsquares are 5, 8, 11, 13, 15, 18, 21, 23, 25, 27, 29, 32, 35, 37, ...
%H A256917 Colin Barker and Charles R Greathouse IV, <a href="/A256917/b256917.txt">Table of n, a(n) for n = 1..10000</a> (first 800 terms from Barker)
%e A256917 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.
%t A256917 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 *)
%t A256917 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 *)
%o A256917 (PARI)
%o A256917 a256917(maxp) = {
%o A256917   ps=[2];
%o A256917   k=1; while((t=2*k^2-1)<=maxp, k++; if(isprime(t), ps=setunion(ps, [t])));
%o A256917   k=1; while((t=2*k^2+1)<=maxp, k++; if(isprime(t), ps=setunion(ps, [t])));
%o A256917   ps
%o A256917 }
%o A256917 a256917(11000) \\ _Colin Barker_, Apr 23 2015
%o A256917 (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
%Y A256917 Cf. A000037, A066436, A090698, A154670.
%K A256917 nonn,easy
%O A256917 1,1
%A A256917 _Juri-Stepan Gerasimov_, Apr 23 2015