A219978 Numbers k (>= 1) such that A007781(k-1) = k^k - (k-1)^(k-1) is semiprime.

5, 6, 13, 16, 18, 21, 22, 28, 29, 37, 46, 60, 71, 84

Offset

1,1

Comments

This is to A072164 as semiprimes A001358 are to primes A000040. Can thus be called power difference semiprimes.

a(15) >= 115, as 115^115 - 114^114 is a 237-digit composite number with no known factors. - Tyler Busby, Feb 12 2023

Links

Table of n, a(n) for n=1..14.

Eric W. Weisstein, Power Difference Prime

Formula

{ k : A007781(k-1) in A001358 }.

Example

a(1) = 5 because 5^5 - 4^4 = 2869 = 19 * 151 is semiprime.
a(2) = 6 because 6^6 - 5^5 = 43531 = 101 * 431.
a(3) = 13 because 13^13 - 12^12 = 293959006143997 = 28201 * 10423708597.
a(4) = 16 because 16^16 - 15^15 = 18008850183328692241 = 109 * 165218809021364149.

Mathematica

Flatten[Position[Differences[Table[n^n, {n, 85}]], _?(PrimeOmega[#]==2&)]]+1 (* Harvey P. Dale, Aug 29 2021 *)

Prog

(PARI) isok(n) = bigomega(n^n - (n-1)^(n-1)) == 2; \\ Michel Marcus, Feb 11 2020

Crossrefs

Cf. A001358, A072164, A007781.

Sequence in context: A061437 A067245 A059176 * A326657 A303139 A322611

Adjacent sequences: A219975 A219976 A219977 * A219979 A219980 A219981

Keyword

nonn,more

Author

Jonathan Vos Post, Dec 02 2012

Extensions

a(9)-a(13) from Charles R Greathouse IV, Dec 02 2012

a(14) from Charles R Greathouse IV, Dec 04 2012

Status

approved