cp's OEIS Frontend

A332534 Numbers that are not of the form prime + 2^(2^k) + m! with k >= 0, m >= 0.

%I A332534 #24 Nov 26 2020 12:19:05
%S A332534 1,2,3,4,38,68,80,98,122,128,146,150,158,164,188,192,206,212,218,220,
%T A332534 222,224,248,252,278,290,292,302,306,308,326,332,338,344,368,374,380,
%U A332534 398,410,416,428,432,440,458,476,488,500,510,518,522,530,532,536,542
%N A332534 Numbers that are not of the form prime + 2^(2^k) + m! with k >= 0, m >= 0.
%H A332534 Alois P. Heinz, <a href="/A332534/b332534.txt">Table of n, a(n) for n = 1..10000</a>
%H A332534 Christian Elsholtz, Florian Luca, and Stefan Planitzer, <a href="https://doi.org/10.1007/s11139-017-9972-8">Romanov type problems</a>, The Ramanujan Journal 47.2 (2018): 267-289.
%p A332534 q:= proc(n) local k, m;
%p A332534       for k from 0 while 2^(2^k)<n do
%p A332534         for m while 2^(2^k)+m!<n do
%p A332534           if isprime(n-2^(2^k)-m!) then return false fi:
%p A332534         od
%p A332534       od; true
%p A332534     end:
%p A332534 select(q, [$1..600])[];  # _Alois P. Heinz_, Feb 15 2020
%t A332534 q[n_] := Module[{k, m}, For[k = 0, 2^(2^k) < n, k++, For[m = 1, 2^(2^k) + m! < n, m++, If[PrimeQ[n - 2^(2^k) - m!] , Return[False]]]]; True];
%t A332534 Select[Range[600], q] (* _Jean-François Alcover_, Nov 26 2020, after _Alois P. Heinz_ *)
%Y A332534 Cf. A218044, A332379, A332535.
%K A332534 nonn
%O A332534 1,2
%A A332534 _N. J. A. Sloane_, Feb 15 2020