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

5, 127, 163, 179, 191, 193, 223, 239, 251, 269, 311, 337, 389, 419, 431, 457, 491, 547, 557, 569, 599, 613, 653, 659, 673, 683, 719, 739, 787, 821, 839, 853, 883, 911, 929, 953, 967, 977, 1117, 1123, 1201, 1229, 1249, 1283, 1289, 1297, 1303, 1327, 1381, 1409, 1423, 1439, 1451, 1471, 1481, 1499

Offset: 1

Author

Reinhard Zumkeller, Jan 17 2006

Keywords

• nonn

Examples

			5 = 2+3 belongs to the sequence, but 23 = 2^2+19^1 = 2^4+7^1 does not.
		

Crossrefs

Subsequence of A115232. Cf. A115230, A115231.

Cf. A000079, A061345.

Programs

Mathematica

maxp = 1500; Clear[cnt]; cnt[_] = 0;
pp = Prime[Range[PrimePi[maxp]]];
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]}
];
Select[pp, cnt[#] == 1&] (* Jean-François Alcover, Aug 04 2018 *)

Extensions

Recomputed (based on recomputation of A115230) by R. J. Mathar and Reinhard Zumkeller, Apr 29 2010.

Edited by N. J. A. Sloane, Apr 30 2010

Data corrected by Jean-François Alcover, Aug 04 2018