A084442 Primes that can be written uniquely as 1+p+p^k, p prime and k > 0.

5, 13, 19, 23, 47, 59, 67, 83, 107, 167, 179, 227, 263, 307, 347, 359, 383, 467, 479, 503, 563, 587, 631, 719, 733, 839, 863, 887, 983, 1019, 1187, 1283, 1307, 1319, 1367, 1439, 1487, 1523, 1619, 1723, 1823, 1907, 2027, 2039, 2063, 2099, 2207, 2447, 2459

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

A084440(a(n)) = 1.

Mathematica

f[p_] := Module[{qs = FactorInteger[p - 1][[;; , 1]]}, Sum[Boole[p - q - 1 == q^IntegerExponent[p - q - 1, q]], {q, qs}]]; f[2] = 0; Select[Prime[Range[400]], f[#] == 1 &] (* Amiram Eldar, Mar 25 2025 *)

Crossrefs

Cf. A084440.

Subsequence of A084441.

The safe primes (A005385) are a subsequence.

Sequence in context: A162174 A171603 A118915 * A023270 A279765 A308196

Adjacent sequences: A084439 A084440 A084441 * A084443 A084444 A084445

Keyword

nonn

Author

Reinhard Zumkeller, May 26 2003

Extensions

Corrected by T. D. Noe, Oct 25 2006

Status

approved