A218450 Number of digits of n plus number of digits of n equal to 1, 2, 4, or 8.

2, 2, 1, 2, 1, 1, 1, 2, 1, 3, 4, 4, 3, 4, 3, 3, 3, 4, 3, 3, 4, 4, 3, 4, 3, 3, 3, 4, 3, 2, 3, 3, 2, 3, 2, 2, 2, 3, 2, 3, 4, 4, 3, 4, 3, 3, 3, 4, 3, 2, 3, 3, 2, 3, 2, 2, 2, 3, 2, 2, 3, 3, 2, 3, 2, 2, 2, 3, 2, 2, 3, 3, 2, 3, 2, 2, 2, 3, 2, 3, 4, 4, 3, 4, 3, 3, 3

Offset: 1

Author

David Williams, Oct 28 2012

Keywords

• nonn
• easy
• base

Links

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

Programs

Maple

f:= proc(n) local L;
  L:= convert(n,base,10);
  nops(L) + numboccur(L,{1,2,4,8})
end proc:
map(f, [$1..100]); # Robert Israel, Apr 29 2021

Mathematica

Table[d = IntegerDigits[n]; Length[d] + Count[d, 1] + Count[d, 2] + Count[d, 4] + Count[d, 8], {n, 100}] (* T. D. Noe, Nov 16 2012 *)
Table[IntegerLength[n]+Total[DigitCount[n,10,{1,2,4,8}]],{n,100}] (* Harvey P. Dale, Aug 03 2021 *)

PARI

a(n) = my(d = digits(n)); #d + #select(x->((x==1) || (x==2) || (x==4) || (x==8)), d); \\ Michel Marcus, Jan 31 2016

Formula

lim inf a(n)/log_10 n = 1; lim sup a(n)/log_10 n = 2.