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%I #29 Feb 16 2018 03:47:09
%S 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,
%T 53,54,55,58,70,72,75,80,81,82,83,85,93,95,128,149,152,170,171,174,
%U 184,185,187,188,189,194,198,201,203,210,212,215,217,233,235,238,242,245
%N 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.
%C From the first 3000 primes, only 179 are terms.
%C From the first 3000 integers, only 343 are terms.
%t 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]=={}&]
%t 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 *)
%o (PARI) has(n)=!setsearch(Set(digits(n)),6)
%o 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
%Y Cf. A052414, A104419, A104420, A104421, A104422, A104423, A104424, A104425, A104427, A104428.
%K nonn,base
%O 1,2
%A _Zak Seidov_, Mar 07 2005
%E Definition modified (at the suggestion of _N. J. A. Sloane_) by _Harvey P. Dale_, Feb 10 2018
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