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

1,1

Links

Table of n, a(n) for n=1..56.

Example

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

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 *)

Crossrefs

Subsequence of A115232. Cf. A115230, A115231.

Cf. A000079, A061345.

Sequence in context: A059486 A071196 A357133 * A157438 A142803 A208859

Adjacent sequences: A115230 A115231 A115232 * A115234 A115235 A115236

Keyword

nonn

Author

Reinhard Zumkeller, Jan 17 2006

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

Status

approved