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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
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.
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
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