A084445 Primes that cannot be written as 1+p+p^k, p prime and k > 0.

2, 3, 17, 29, 37, 41, 43, 53, 61, 71, 73, 79, 89, 97, 101, 103, 109, 113, 127, 137, 139, 149, 151, 157, 163, 173, 181, 191, 193, 197, 199, 211, 223, 229, 233, 239, 241, 251, 257, 269, 271, 277, 281, 283, 293, 311, 313, 317, 331, 337, 349, 353, 367, 373, 379

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

A084440(a(n)) = 0.

Maple

N:= 1000: # for terms <= N
S:= select(isprime, {2, seq(i, i=3..N, 2)}):
for i from 1 do
  p:= ithprime(i);
  if 2*p+1 > N then break fi;
  for k from 1 do
    q:= 1+p+p^k;
    if q > N then break fi;
    S:= S minus {q};
  od;
od:
sort(convert(S, list)); # Robert Israel, Dec 13 2023

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[75]], f[#] == 0 &] (* Amiram Eldar, Mar 25 2025 *)

Crossrefs

Cf. A084440, A084441.

Sequence in context: A029876 A248716 A228201 * A215303 A215280 A219559

Adjacent sequences: A084442 A084443 A084444 * A084446 A084447 A084448

Keyword

nonn

Author

Reinhard Zumkeller, May 26 2003

Status

approved