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

1,2

Comments

From the first 3000 primes, only 179 are terms.

From the first 3000 integers, only 343 are terms.

Links

Table of n, a(n) for n=1..63.

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A213622 A246847 A193406 * A097044 A198330 A232779

Adjacent sequences: A104423 A104424 A104425 * A104427 A104428 A104429

Keyword

nonn,base

Author

Zak Seidov, Mar 07 2005

Extensions

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

Status

approved