A084441 Primes that can be written as 1+p+p^k, p prime and k > 0.

5, 7, 11, 13, 19, 23, 31, 47, 59, 67, 83, 107, 131, 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

Offset

1,1

Links

Jason Yuen, Table of n, a(n) for n = 1..10000

Formula

A084440(a(n)) > 0.

Example

prime(6) = 13 = 1+3+3^2, therefore 13 is a term; A084440(6) = 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[330]], f[#] > 0 &] (* Amiram Eldar, Mar 25 2025 *)

Crossrefs

Cf. A084440, A084442, A084443, A084444, A084445.

The safe primes (A005385) are a subsequence.

Sequence in context: A375170 A216746 A391049 * A180950 A112397 A081759

Adjacent sequences: A084438 A084439 A084440 * A084442 A084443 A084444

Keyword

nonn,easy

Author

Reinhard Zumkeller, May 26 2003

Status

approved