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

1,3

Comments

Some of the larger entries may only correspond to probable primes.

Links

Table of n, a(n) for n=1..20.

Example

a(3)=3 because 496 + 3 is a prime.

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}]

Crossrefs

Cf. A000043, A000396, A061644, A078097.

Sequence in context: A189799 A300946 A364298 * A139429 A293699 A258200

Adjacent sequences: A078093 A078094 A078095 * A078097 A078098 A078099

Keyword

nonn,hard,more

Author

Jason Earls, Dec 01 2002

Extensions

Edited and extended by Robert G. Wilson v, Dec 03 2002

a(19)-a(20) from Jinyuan Wang, Jun 13 2020

Status

approved