A105717 Smallest Fibonacci number that has 7 in the n-th position of the decimal representation.

377, 377, 6765, 17711, 75025, 5702887, 267914296, 2971215073, 701408733, 7778742049, 27777890035288, 27777890035288, 17167680177565, 72723460248141, 51680708854858323072, 37889062373143906, 679891637638612258

Offset: 0

Author

Reinhard Zumkeller, Apr 18 2005

Keywords

• nonn
• base

Comments

a(n) = A000045(A105707(n)).

The n-th position is counted from the right. - Harvey P. Dale, Jul 22 2024

Examples

			n=3: A105700(3)=22, a(3)=A000045(22)=17711->1[7]711;
n=4: A105700(4)=25, a(4)=A000045(25)=75025->[7]5025.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..995
• Eric Weisstein's World of Mathematics, Fibonacci Number

Crossrefs

Cf. A105711, A072351, A105712, A105713, A105714, A105715, A105716, A105718, A105719.

Programs

Maple

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

Mathematica

With[{fibs=Fibonacci[Range[150]]},Table[SelectFirst[fibs,NumberDigit[#,n-1]==7&],{n,20}]] (* Harvey P. Dale, Jul 22 2024 *)

Extensions

Definition corrected by Robert Israel, Jun 01 2020