A276567 Odd squares not of the form p + 2^k with p prime.

1, 40401, 62001, 96721, 121801, 192721, 326041, 410881, 555025, 660969, 683929, 772641, 786769, 822649, 1343281, 1390041, 1530169, 1739761, 1885129, 1923769, 1962801, 2283121, 2544025, 2913849, 3207681, 3214849, 3352561, 3396649, 3613801, 3775249, 3853369, 4060225

Offset

1,2

Comments

The sequence contains also Sierpiński numbers (i.e., 4521731193704761, 60428287050225649).

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

A006285 INTERSECT A016754.

Maple

filter:= proc(n) local k;
   for k from 0 to ilog2(n) do
     if isprime(n - 2^k) then return false fi
   od:
   true
end proc:
select(filter, [seq((2*i+1)^2, i=0..10^4)]); # Robert Israel, Sep 07 2016

Mathematica

filterQ[n_] := Module[{k}, For[k = 0, k <= Log[2, n], k++, If[PrimeQ[n - 2^k], Return[False]]]; True];
Select[Table[(2i+1)^2, {i, 0, 10^4}], filterQ] (* Jean-François Alcover, Oct 06 2020, after Maple *)

Prog

(Magma) lst:=[]; for s in [1..2015 by 2] do n:=s^2; x:=0; repeat x+:=1; a:=n-2^x; until a lt 1 or IsPrime(a); if a lt 1 then Append(~lst, n); end if; end for; lst;

Crossrefs

Cf. A006285, A016754.

Sequence in context: A229675 A250905 A250949 * A216291 A216290 A237970

Adjacent sequences: A276564 A276565 A276566 * A276568 A276569 A276570

Keyword

nonn

Author

Arkadiusz Wesolowski, Sep 06 2016

Status

approved