A084444 Primes that can be written as 1+p+p^k, p prime and k > 1.

7, 11, 13, 19, 31, 67, 131, 307, 631, 733, 1723, 3541, 4099, 4931, 5113, 8011, 10303, 14653, 17293, 19687, 24419, 28057, 30103, 32771, 59053, 65539, 68963, 86143, 147073, 148931, 262147, 357983, 459007, 492103, 552793, 571871, 579883, 598303, 684757, 704761

Offset

1,1

Links

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

Formula

A084440(a(n)) > 0.

Example

729 = 1+3+3^6.

Mathematica

f[p_] := Module[{qs = FactorInteger[p - 1][[;; , 1]], k}, Sum[k = IntegerExponent[p - q - 1, q]; Boole[k > 1 && p - q - 1 == q^k], {q, qs}]]; f[2] = 0; Select[Prime[Range[60000]], f[#] > 0 &] (* Amiram Eldar, Mar 25 2025 *)

Crossrefs

Cf. A084440.

Subsequence of A084441.

Sequence in context: A059637 A059308 A075521 * A395982 A081091 A027901

Adjacent sequences: A084441 A084442 A084443 * A084445 A084446 A084447

Keyword

nonn

Author

Reinhard Zumkeller, May 26 2003

Extensions

More terms from David Wasserman, Dec 29 2004

Status

approved