A084046 Smallest prime p such that p + n is an n-th power, or 0 if no such number exists; i.e., smallest prime of the form k^n - n.

2, 2, 5, 0, 1019, 15619, 2799359999993, 6553, 503, 16679880978191, 8293509467471861, 244140613, 8179, 152736582765019941952958691637187, 5097655355238390956017, 0, 18909044154723310956357640154206945542127, 5559917313492231463, 524269, 3486784381, 2097131

Offset

1,1

Comments

a(4n^2) = 0. Conjecture: if a(k) = 0 then k is an even square.

Conjecture is false: a(27) = 0 because k^27-27 = (k^9-3) * (k^18 + 3*k^9 + 9). - Sean A. Irvine, Mar 07 2026

Links

Sean A. Irvine, Table of n, a(n) for n = 1..150

Example

a(5) = 1019 as 1019 + 5 = 1024 = 4^5.

Crossrefs

Cf. A084047.

Sequence in context: A393072 A194123 A011342 * A200493 A267857 A173169

Adjacent sequences: A084043 A084044 A084045 * A084047 A084048 A084049

Keyword

base,nonn

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 26 2003

Extensions

More terms from Ray Chandler, Jun 16 2003

More terms from Sean A. Irvine, Mar 07 2026

Status

approved