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Search: a105719 -id:a105719
Displaying 1-10 of 10 results found. page 1
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A072351 Smallest n-digit Fibonacci number. +10
12
1, 13, 144, 1597, 10946, 121393, 1346269, 14930352, 102334155, 1134903170, 12586269025, 139583862445, 1548008755920, 10610209857723, 117669030460994, 1304969544928657, 14472334024676221, 160500643816367088, 1100087778366101931, 12200160415121876738 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..1000
FORMULA
A072351(n) = floor(1/2 + phi^ceiling((n*log(10) + (1/2)*log(5))/log(phi))/sqrt(5)). - Franklin T. Adams-Watters, May 27 2011
EXAMPLE
a(3)=144, as 144 is smallest 3-digit Fibonacci number.
MAPLE
F:= proc(n) option remember; local f;
f:= `if`(n=1, [1$2], F(n-1));
do f:= [f[2], f[1]+f[2]];
if length(f[1])<length(f[2]) then break fi
od; f
end:
a:= n-> `if`(n=1, 1, F(n-1)[2]):
seq(a(n), n=1..25); # Alois P. Heinz, Mar 10 2016
MATHEMATICA
a[n_] := Fibonacci[Ceiling[k /. FindRoot[Log[10, Fibonacci[k]] == n-1, {k, 1}]]]; Array[a, 20] (* Jean-François Alcover, Jan 18 2017 *)
PROG
(PARI) A072351(n, phi=(sqrt(5)+1)/2)=round(phi^ceil((n*log(10)+log(5)/2)/log(phi))/sqrt(5)) \\ Franklin T. Adams-Watters, May 27 2011
(Python)
def A072351_list(n):
list = [1]
x, y = 1, 1
while len(list) < n:
if len(str(x)) < len(str(y)):
list.append(y)
x, y = y, x + y
return list
print(A072351_list(20)) # M. Eren Kesim, Jun 28 2021
CROSSREFS
Cf. A072352, A105710, A105712, A105713, A105714, A105715, A105716, A105717, A105718, A105719.
KEYWORD
base,nonn
AUTHOR
Shyam Sunder Gupta, Jul 17 2002
STATUS
approved
A105717 Smallest Fibonacci number that has 7 in the n-th position of the decimal representation +10
11
377, 377, 6765, 17711, 75025, 5702887, 267914296, 2971215073, 701408733, 7778742049, 27777890035288, 27777890035288, 17167680177565, 72723460248141, 51680708854858323072, 37889062373143906, 679891637638612258 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
a(n) = A000045(A105707(n)).
The n-th position is counted from the right. - Harvey P. Dale, Jul 22 2024
LINKS
Robert Israel, Table of n, a(n) for n = 0..995
Eric Weisstein's World of Mathematics, Fibonacci Number
EXAMPLE
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.
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 *)
CROSSREFS
Cf. A105711, A072351, A105712, A105713, A105714, A105715, A105716, A105718, A105719.
KEYWORD
nonn,base
AUTHOR
Reinhard Zumkeller, Apr 18 2005
EXTENSIONS
Definition corrected by Robert Israel, Jun 01 2020
STATUS
approved
A105709 Smallest m such that 9 is at the n-th position of the decimal representation of the m-th Fibonacci number. +10
10
11, 17, 16, 50, 27, 36, 35, 66, 47, 55, 58, 59, 81, 70, 78, 83, 83, 95, 94, 111, 102, 148, 114, 140, 125, 126, 138, 137, 145, 150, 150, 163, 161, 183, 169, 205, 189, 191, 192, 193, 215, 204, 216, 212, 223, 224, 228, 243, 236, 250, 258, 257, 267, 260, 270, 271 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
A105719(n) = A000045(a(n)).
LINKS
Table of n, a(n) for n=0..55.
Eric Weisstein's World of Mathematics, Fibonacci Number
EXAMPLE
n=3: a(3)=50,
A000045(50)=A105710(3)=12586269025->1258626[9]025;
n=4: a(4)=27, A000045(27)=A105710(4)=196418->1[9]6418.
CROSSREFS
Cf. A105701, A072354, A105702, A105703, A105704, A105705, A105706, A105707, A105708.
KEYWORD
nonn,base
AUTHOR
Reinhard Zumkeller, Apr 18 2005
STATUS
approved
A105712 Smallest m such that 2 is at the n-th position of the decimal representation of the m-th Fibonacci number. +10
10
2, 21, 233, 2584, 28657, 9227465, 2178309, 24157817, 267914296, 2971215073, 20365011074, 225851433717, 2504730781961, 27777890035288, 19740274219868223167, 2111485077978050, 23416728348467685 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
a(n) = A000045(A105702(n)).
LINKS
Table of n, a(n) for n=0..16.
Eric Weisstein's World of Mathematics, Fibonacci Number
EXAMPLE
n=3: A105700(3)=18, a(3)=A000045(18)=2584->[2]584;
n=4: A105700(4)=23, a(4)=A000045(23)=28657->[2]8657.
CROSSREFS
Cf. A105711, A072351, A105713, A105714, A105715, A105716, A105717, A105718, A105719.
KEYWORD
nonn,base
AUTHOR
Reinhard Zumkeller, Apr 18 2005
STATUS
approved
A105713 Smallest m such that 3 is at the n-th position of the decimal representation of the m-th Fibonacci number. +10
10
3, 34, 377, 1134903170, 832040, 317811, 3524578, 39088169, 20365011074, 53316291173, 32951280099, 365435296162, 7540113804746346429, 31940434634990099905, 308061521170129, 3416454622906707 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
a(n) = A000045(A105703(n)).
LINKS
Table of n, a(n) for n=0..15.
Eric Weisstein's World of Mathematics, Fibonacci Number
EXAMPLE
n=3: A105700(3)=45,
a(3)=A000045(45)=1134903170->113490[3]170;
n=4: A105700(4)=30, a(4)=A000045(30)=832040->8[3]2040.
CROSSREFS
Cf. A105711, A072351, A105712, A105714, A105715, A105716, A105717, A105718, A105719.
KEYWORD
nonn,base
AUTHOR
Reinhard Zumkeller, Apr 18 2005
STATUS
approved
A105714 Smallest m such that 4 is at the n-th position of the decimal representation of the m-th Fibonacci number. +10
10
34, 144, 196418, 4181, 46368, 433494437, 14930352, 1304969544928657, 433494437, 4807526976, 1548008755920, 498454011879264, 4052739537881, 44945570212853, 498454011879264, 14472334024676221, 7540113804746346429 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
a(n) = A000045(A105704(n)).
LINKS
Table of n, a(n) for n=0..16.
Eric Weisstein's World of Mathematics, Fibonacci Number
EXAMPLE
n=3: A105700(3)=19, a(3)=A000045(19)=4181->[4]181;
n=4: A105700(4)=24, a(4)=A000045(24)=46368->[4]6368.
CROSSREFS
Cf. A105711, A072351, A105712, A105713, A105715, A105716, A105717, A105718, A105719.
KEYWORD
nonn,base
AUTHOR
Reinhard Zumkeller, Apr 18 2005
STATUS
approved
A105715 Smallest m such that 5 is at the n-th position of the decimal representation of the m-th Fibonacci number. +10
10
5, 55, 1597, 75025, 24157817, 514229, 5702887, 32951280099, 12586269025, 225851433717, 53316291173, 591286729879, 61305790721611591, 135301852344706746049, 5527939700884757, 5527939700884757 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
a(n) = A000045(A105705(n)).
LINKS
Table of n, a(n) for n=0..15.
Eric Weisstein's World of Mathematics, Fibonacci Number
EXAMPLE
n=3: A105700(3)=25, a(3)=A000045(25)=75025->7[5]025;
n=4: A105700(4)=37, a(4)=A000045(37)=24157817->241[5]7817.
CROSSREFS
Cf. A105711, A072351, A105712, A105713, A105714, A105716, A105717, A105718, A105719.
KEYWORD
nonn,base
AUTHOR
Reinhard Zumkeller, Apr 18 2005
STATUS
approved
A105716 Smallest m such that 6 is at the n-th position of the decimal representation of the m-th Fibonacci number. +10
10
10946, 6765, 610, 6765, 12586269025, 14472334024676221, 1836311903, 63245986, 17167680177565, 86267571272, 365435296162, 10610209857723, 6557470319842, 2880067194370816120, 259695496911122585, 6356306993006846248183 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
a(n) = A000045(A105706(n)).
LINKS
Table of n, a(n) for n=0..15.
Eric Weisstein's World of Mathematics, Fibonacci Number
EXAMPLE
n=3: A105700(3)=20, a(3)=A000045(20)=6765->[6]765;
n=4: A105700(4)=50,
a(4)=A000045(50)=12586269025->125862[6]9025.
CROSSREFS
Cf. A105711, A072351, A105712, A105713, A105714, A105715, A105717, A105718, A105719.
KEYWORD
nonn,base
AUTHOR
Reinhard Zumkeller, Apr 18 2005
STATUS
approved
A105718 Smallest Fibonacci number such that 8 is at the n-th position (from the right) of its decimal representation. +10
10
8, 89, 317811, 28657, 39088169, 832040, 7778742049, 12586269025, 1836311903, 1548008755920, 86267571272, 99194853094755497, 308061521170129, 37889062373143906, 806515533049393, 8944394323791464, 2880067194370816120 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
a(n) = A000045(A105708(n)).
LINKS
Table of n, a(n) for n=0..16.
Eric Weisstein's World of Mathematics, Fibonacci Number
EXAMPLE
n=3: A105700(3)=23, a(3)=A000045(23)=28657->2[8]657;
n=4: A105700(4)=38, a(4)=A000045(38)=39088169->390[8]8169.
CROSSREFS
Cf. A105711, A072351, A105712, A105713, A105714, A105715, A105716, A105717, A105719.
KEYWORD
nonn,base
AUTHOR
Reinhard Zumkeller, Apr 18 2005
EXTENSIONS
Definition corrected by Robert Israel, Apr 25 2021
STATUS
approved
A105711 Smallest m such that 0 is at the n-th position of the decimal representation of the m-th Fibonacci number. +10
8
0, 2178309, 75025, 10946, 5702887, 39088169, 2504730781961, 102334155, 1548008755920, 20365011074, 2504730781961, 4052739537881, 10610209857723, 308061521170129, 1100087778366101931, 160500643816367088 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
a(n) = A000045(A105701(n)).
LINKS
Table of n, a(n) for n=0..15.
Eric Weisstein's World of Mathematics, Fibonacci Number
EXAMPLE
n=3: A105701(3)=21, a(3)=A000045(21)=10946->1[0]946;
n=4: A105701(4)=34, a(4)=A000045(34)=5702887->57[0]2887.
CROSSREFS
Cf. A072351, A105712, A105713, A105714, A105715, A105716, A105717, A105718, A105719.
KEYWORD
nonn,base
AUTHOR
Reinhard Zumkeller, Apr 18 2005
STATUS
approved
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Last modified August 30 00:57 EDT 2024. Contains 375520 sequences. (Running on oeis4.)