A104420 -id:A104420

Search: a104420 -id:a104420

Displaying 1-1 of 1 result found.

page 1

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.

+10
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

(list; graph; refs; listen; history; text; internal format)

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.

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

page 1

Search completed in 0.005 seconds