

A115233


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


3



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
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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&] (* JeanFrançois Alcover, Aug 04 2018 *)


CROSSREFS

Subsequence of A115232. Cf. A115230, A115231.
Cf. A000079, A061345.
Sequence in context: A015476 A059486 A071196 * 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 JeanFrançois Alcover, Aug 04 2018


STATUS

approved



