A078096 Least m such that P + m is a prime, where P is the n-th perfect number.
1, 1, 3, 19, 1, 7, 1, 105, 37, 163, 73, 43, 45, 649, 3753, 5323, 423, 3123, 9981, 12943
Offset: 1
Examples
a(3)=3 because 496 + 3 is a prime.
Programs
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Mathematica
e (* from A000043 *) = {2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, ...}; NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; Do[p = 2^(e[[n]] - 1)*(2^e[[n]] - 1); Print[NextPrim[p] - p], {n, 1, 20}]
Extensions
Edited and extended by Robert G. Wilson v, Dec 03 2002
a(19)-a(20) from Jinyuan Wang, Jun 13 2020
Comments