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

Author

Zak Seidov, Mar 07 2005

Keywords

• nonn
• base

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

Crossrefs

Cf. A104419-A104428.

Programs

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 *)

Extensions

Name edited by Robert Israel, Apr 23 2020