A078097 Least m such that P - m is prime, where P is the n-th perfect number.

1, 5, 5, 5, 5, 17, 9, 65, 93, 129, 627, 111, 407, 795, 377, 1509, 257, 5207, 1233, 8537, 3917, 20253, 4613, 15435, 5619, 43823

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..26.

Mathematica

e (* from A000043 *) = {2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, ...}; PrevPrim[n_] := Block[{k = n - 1}, While[ !PrimeQ[k], k-- ]; k]; Do[p = 2^(e[[n]] - 1)*(2^e[[n]] - 1); Print[p - PrevPrim[p]], {n, 1, 20}]
#-NextPrime[#, -1]&/@PerfectNumber[Range[15]] (* The program generates the first 15 terms of the sequence. To generate more, increase the Range constant but the program may take a long time to run. *) (* Harvey P. Dale, Nov 22 2023 *)

Crossrefs

Cf. A061644, A000396, A000043.

Sequence in context: A076407 A134701 A291655 * A285243 A339704 A282209

Adjacent sequences: A078094 A078095 A078096 * A078098 A078099 A078100

Keyword

hard,more,nonn

Author

Jason Earls, Dec 01 2002

Extensions

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

a(19)-a(26) from Donovan Johnson, Feb 22 2008

Status

approved