A085753 Least k such that n^n + k is a semiprime.

3, 0, 6, 3, 2, 5, 6, 3, 4, 3, 6, 31, 6, 3, 4, 1, 20, 19, 28, 3, 8, 3, 60, 5, 16, 15, 46, 3, 2, 7, 12, 13, 4, 3, 18, 3, 9, 3, 32, 7, 6, 37, 30, 61, 2, 81, 26, 5, 34, 79, 62, 6, 44, 5, 16, 15, 10, 133, 12, 31, 28, 49, 26, 21, 92, 43, 76, 67, 38, 57, 36, 43, 21, 115, 2, 25, 74, 179, 28, 27, 52, 15

Offset: 1

Author

Jason Earls, Jul 21 2003

Keywords

• nonn

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..100
• Dario Alejandro Alpern, Factorization using the Elliptic Curve Method

Crossrefs

Cf. A001358 (semiprimes), A089542, A089543, A089544.

Programs

Mathematica

PrimeFactorExponentsAdded[n_] := Plus @@ Flatten[ Table[ # [[2]], {1}] & /@ FactorInteger[n]]; f[n_] := Block[{k = 0}, While[ PrimeFactorExponentsAdded[n^n + k] != 2, k++ ]; k]; Table[ f[n], {n, 1, 40}]
Table[Module[{k=0,c=n^n},While[PrimeOmega[c+k]!=2,k++];k],{n,82}] (* Harvey P. Dale, Aug 02 2025 *)

PARI

a(n) = my(k=0); while (bigomega(n^n+k) != 2, k++); k; \\ Michel Marcus, Jul 21 2020

Extensions

Edited and extended by Robert G. Wilson v, Aug 14 2003

Corrected and extended by Ray Chandler, Nov 22 2003

a(69)-a(82) from Max Alekseyev, Jun 13 2009

a(52) and a(73) corrected by Sean A. Irvine, Jul 20 2020