Mersenne exponents that are not part of a twin prime pair.
2, 89, 127, 607, 2203, 2281, 3217, 4253, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 25964951, 30402457, 32582657
1
This is the complement of the Mersenne exponents given in S000869.
T. D. Noe, Plot of 28 terms
Kent D. Boklan and John H. Conway, Expect at most one billionth of a new Fermat Prime!, arXiv 1605.01371 (May 04 2016)
(Mma) p = {2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951, 30402457, 32582657}; Complement[p, Select[p, PrimeQ[# - 2] || PrimeQ[# + 2] &]]
Cf. A000043 (Mersenne exponents), S000869.
nonn,more
T. D. Noe, May 05 2016