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A115233 Primes p which have a unique representation as p = 2^i + q^j where i >= 0, j >= 1, q = odd prime.

%I A115233 #10 Aug 04 2018 14:34:52
%S A115233 5,127,163,179,191,193,223,239,251,269,311,337,389,419,431,457,491,
%T A115233 547,557,569,599,613,653,659,673,683,719,739,787,821,839,853,883,911,
%U A115233 929,953,967,977,1117,1123,1201,1229,1249,1283,1289,1297,1303,1327,1381,1409,1423,1439,1451,1471,1481,1499
%N A115233 Primes p which have a unique representation as p = 2^i + q^j where i >= 0, j >= 1, q = odd prime.
%e A115233 5 = 2+3 belongs to the sequence, but 23 = 2^2+19^1 = 2^4+7^1 does not.
%t A115233 maxp = 1500; Clear[cnt]; cnt[_] = 0;
%t A115233 pp = Prime[Range[PrimePi[maxp]]];
%t A115233 Do[p = 2^i + q^j; If[p <= maxp && PrimeQ[p], cnt[p] = cnt[p] + 1], {i, 0, Log[2, maxp] // Ceiling}, {j, 1, Log[3, maxp] // Ceiling}, {q, Rest[pp]}
%t A115233 ];
%t A115233 Select[pp, cnt[#] == 1&] (* _Jean-François Alcover_, Aug 04 2018 *)
%Y A115233 Subsequence of A115232. Cf. A115230, A115231.
%Y A115233 Cf. A000079, A061345.
%K A115233 nonn
%O A115233 1,1
%A A115233 _Reinhard Zumkeller_, Jan 17 2006
%E A115233 Recomputed (based on recomputation of A115230) by _R. J. Mathar_ and _Reinhard Zumkeller_, Apr 29 2010.
%E A115233 Edited by _N. J. A. Sloane_, Apr 30 2010
%E A115233 Data corrected by _Jean-François Alcover_, Aug 04 2018