A104426 Numbers k such that the digit 6 does not appear in the decimal expansion of k, Pk, Pk+k, Pk-k, or Pk*k, where Pk is the k-th prime.

1, 3, 4, 7, 8, 9, 10, 11, 12, 13, 20, 21, 22, 25, 30, 33, 35, 37, 41, 43, 44, 48, 50, 51, 52, 53, 54, 55, 58, 70, 72, 75, 80, 81, 82, 83, 85, 93, 95, 128, 149, 152, 170, 171, 174, 184, 185, 187, 188, 189, 194, 198, 201, 203, 210, 212, 215, 217, 233, 235, 238, 242, 245

Offset: 1

Author

Zak Seidov, Mar 07 2005

Keywords

• nonn
• base

Comments

From the first 3000 primes, only 179 are terms.

From the first 3000 integers, only 343 are terms.

Crossrefs

Cf. A052414, A104419, A104420, A104421, A104422, A104423, A104424, A104425, A104427, A104428.

Programs

Mathematica

id[x_]:=IntegerDigits[x];pr[i_]:=Prime[i];ra=Range[3000];A104426=Select[ra, Position[Union[id[ # ], id[pr[ # ]], id[pr[ # ]+# ], id[pr[ # ]-# ], id[pr[ # ]*# ]], 6]=={}&]
slQ[n_]:=Module[{p=Prime[n]},Union[DigitCount[#,10,6]&/@{n,p,p+n,p-n, p*n}] == {0}]; Select[Range[250],slQ] (* Harvey P. Dale, Feb 01 2018 *)

PARI

has(n)=!setsearch(Set(digits(n)),6)
is(n,p=prime(n))=has(n) && has(p) && has(p+n) && has(p-n) && has(p*n) \\ Charles R Greathouse IV, Feb 01 2018

Extensions

Definition modified (at the suggestion of N. J. A. Sloane) by Harvey P. Dale, Feb 10 2018