A078096 - OEIS

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

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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