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A367186 Numbers that can be written as 2^k + prime in more than one way.

%I A367186 #27 Nov 29 2023 13:05:56
%S A367186 4,6,7,9,11,13,15,18,19,21,23,25,27,31,33,35,37,39,43,45,47,49,51,55,
%T A367186 57,61,63,67,69,71,73,75,77,79,81,83,85,87,91,93,95,99,101,103,105,
%U A367186 107,109,111,113,115,117,121,123,125,129,131,133,135,139,141,143,145,147,151,153,155
%N A367186 Numbers that can be written as 2^k + prime in more than one way.
%C A367186 Numbers m such that A109925(m) > 1.
%e A367186 4 is a term since 4 = 2^0 + 3 = 2^1 + 2 which is 2 ways.
%e A367186 6 is a term since 6 = 2^0 + 5 = 2^2 + 2.
%o A367186 (PARI) isok(m) = sum(k=0, logint(m,2), isprime(m-2^k)) > 1; \\ _Michel Marcus_, Nov 10 2023
%o A367186 (Python)
%o A367186 from itertools import count, islice
%o A367186 from sympy import isprime
%o A367186 def A367186_gen(startvalue=1): # generator of terms >= startvalue
%o A367186     for n in count(max(startvalue,1)):
%o A367186         c = 0
%o A367186         for i in range(n.bit_length()-1,-1,-1):
%o A367186             if isprime(n-(1<<i)):
%o A367186                 c+=1
%o A367186             if c>1:
%o A367186                 yield n
%o A367186                 break
%o A367186 A367186_list = list(islice(A367186_gen(),30)) # _Chai Wah Wu_, Nov 29 2023
%Y A367186 Subsequence of A118955.
%Y A367186 Cf. A000040, A000079, A109925.
%K A367186 nonn
%O A367186 1,1
%A A367186 _Yuda Chen_, Nov 08 2023