A104424 Numbers n such that n, prime(n), prime(n)+n, prime(n)-n and prime(n)*n all lack the digit 4.

1, 2, 3, 5, 6, 8, 10, 22, 23, 26, 27, 28, 29, 31, 39, 57, 58, 62, 66, 112, 120, 122, 125, 126, 129, 130, 131, 135, 137, 139, 152, 153, 178, 182, 183, 192, 196, 210, 211, 212, 213, 216, 220, 221, 222, 250, 280, 285, 286, 287, 291, 293, 295, 299, 300, 303, 305, 306

Offset

1,2

Comments

From the first 3000 primes, only 289 are such that n, p[n], p[n]+n, p[n]-n and p[n]*n all are 4-less.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

fourless:= n -> not has(4, convert(n, base, 10)):
p:= 1: R:= NULL: count:= 0:
for n from 1 while count < 100 do
  p:= nextprime(p);
  if andmap(fourless, [n, p, p+n, p-n, p*n]) then
    count:= count+1; R:= R, n;
  fi
od:
R; # Robert Israel, Apr 23 2020

Mathematica

id[x_]:=IntegerDigits[x]; pr[i_]:=Prime[i]; ra=Range[3000]; A104424=Select[ra, Position[Union[id[ # ], id[pr[ # ]], id[pr[ # ]+# ], id[pr[ # ]-# ], id[pr[ # ]*# ]], 4]=={}&]
Select[Range[350], Count[Flatten[IntegerDigits/@{#, Prime[#], Prime[ #]+#, Prime[ #]-#, Prime[ #]#}], 4]==0&] (* Harvey P. Dale, Apr 13 2022 *)

Crossrefs

Cf. A104419-A104428.

Sequence in context: A348868 A124145 A188064 * A028806 A351807 A028731

Adjacent sequences: A104421 A104422 A104423 * A104425 A104426 A104427

Keyword

nonn,base

Author

Zak Seidov, Mar 07 2005

Extensions

Name edited by Robert Israel, Apr 23 2020

Status

approved