A105707 Smallest m such that 7 is at the n-th position of the decimal representation of the m-th Fibonacci number.

14, 14, 20, 22, 25, 34, 42, 47, 44, 49, 66, 66, 65, 68, 96, 81, 87, 89, 92, 101, 116, 145, 111, 116, 129, 153, 132, 135, 167, 159, 159, 156, 159, 168, 175, 176, 178, 183, 217, 198, 199, 202, 221, 223, 249, 223, 226, 235, 266, 243, 245, 250, 258, 265, 266, 269

Offset: 0

Author

Reinhard Zumkeller, Apr 18 2005

Keywords

• nonn
• base

Comments

Positions start with the 0th position on the right. - Robert Israel, Jun 01 2020

Examples

			n=3: a(3)=22, A000045(22) = A105710(3) = 17711 -> 1[7]711;
n=4: a(4)=25, A000045(25) = A105710(4) = 75025 -> [7]5025.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..2000
• Eric Weisstein's World of Mathematics, Fibonacci Number

Crossrefs

Cf. A105701, A072354, A105702, A105703, A105704, A105705, A105706, A105708, A105709.

Programs

Maple

N:= 100: # for a(0) to a(N)
F[0]:= 0: F[1]:= 1:
V:= Array(0..N):
count:= 0:
for m from 2 while count < N+1 do
  F[m]:= F[m-1]+F[m-2];
  L:= convert(F[m],base,10);
  M:= select(t -> L[t+1]=7 and V[t]=0, [$0..min(N,nops(L)-1)]);
  count:= count + nops(M);
  V[M]:= m;
od:
convert(V,list); # Robert Israel, Jun 01 2020

Formula

A000045(a(n)) = A105717(n).