A072710 -id:A072710 - cp's OEIS frontend

A105508 Numbers m such that 8 is the leading digit of the m-th Fibonacci number in decimal representation.

6, 11, 30, 54, 73, 78, 97, 121, 140, 145, 164, 188, 207, 231, 255, 274, 298, 322, 341, 365, 389, 408, 432, 451, 456, 475, 499, 518, 523, 542, 566, 585, 590, 609, 633, 652, 676, 700, 719, 743, 767, 786, 810, 834, 853, 877, 896, 901, 920, 944, 963, 968, 987

Offset: 1

Reinhard Zumkeller, Apr 11 2005

			a(1)=6 since the 6th Fibonacci: 8 begins with 8.
a(2)=11 since the 11th Fibonacci: 89 begins with 8.

Cf. A000030, A000045, A072710, A105501, A105502, A105503, A105504, A105505, A105506, A105507, A105509.

Flatten[Position[Fibonacci[Range[1000]],?(First[IntegerDigits[#]]==8&)]] (* _Harvey P. Dale, Jan 04 2015  *)

isok(n) = digits(fibonacci(n))[1] == 8; \\ Michel Marcus, Jan 10 2014

A008963(a(n)) = A000030(A000045(a(n))) = 8.
A105518(a(n)) = A105518(a(n) - 1) + 1.
A000045(a(n)) = A045732(n).
a(n) ~ kn by the equidistribution theorem, where k = log(10)/(log(9) - log(8)) = 19.549378.... - Charles R Greathouse IV, Oct 07 2016

Example and formulas edited by Michel Marcus, Jan 10 2014

A304158 a(n) is the second Zagreb index of the linear phenylene G[n], defined pictorially in the Darafsheh reference (Fig. 3).

Original entry on oeis.org

24, 84, 144, 204, 264, 324, 384, 444, 504, 564, 624, 684, 744, 804, 864, 924, 984, 1044, 1104, 1164, 1224, 1284, 1344, 1404, 1464, 1524, 1584, 1644, 1704, 1764, 1824, 1884, 1944, 2004, 2064, 2124, 2184, 2244, 2304, 2364, 2424, 2484, 2544, 2604, 2664, 2724, 2784, 2844, 2904, 2964

Offset: 1

Emeric Deutsch, May 08 2018

The second Zagreb index of a simple connected graph is the sum of the degree products d(i)d(j) over all edges ij of the graph.

The M-polynomial of the linear phenylene G[n] is M(G[n];x,y) = 6*x^2*y^2 + 4*(n - 1)*x^2*y^3 + 4(n - 1)*x^3*y^3.

			a(1) = 24; indeed, G[1] is a hexagon; we have 6 edges, each with end vertices of degree 2; then the second Zagreb index is 6*2*2 =24.

Colin Barker, Table of n, a(n) for n = 1..1000
O. Bodroza-Pantic, I. Gutman, and S. J. Cyvin, Fibonacci numbers and algebraic structure count of some non-benzenoid conjugated polymers, The Fibonacci Quarterly, 35, 1, 1997, 75-83.
M. R. Darafsheh, Computation of topological indices of some graphs, Acta Appl. Math., 110, 2010, 1225-1235.
E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
P. Gayathri and U. Priyanka, Degree based topological indices of linear phenylene, Internat. J. of Innovative Research in Science, Engineering and Technology, 6, 8, 2017, 16986-16997.
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A016873, A304157.

Subsequence of A121024.

[60*n-36 for n in 1:50] |> println # Bruno Berselli, May 09 2018

Maple
```
seq(60*n - 36, n = 1 .. 40);
```

a(n) = 60*n-36; \\ Altug Alkan, May 09 2018

Vec(12*x*(2 + 3*x)/(1 - x)^2 + O(x^40)) \\ Colin Barker, May 23 2018

a(n) = 60*n - 36.
a(n) = 12 * A016873(n-1). - Alois P. Heinz, May 09 2018
From Bruno Berselli, May 09 2018: (Start)
O.g.f.: 12*x*(2 + 3*x)/(1 - x)^2.
E.g.f.: 12*(3 - 3*exp(x) + 5*x*exp(x)).
a(n) = 2*a(n-1) - a(n-2).
a(n) = A008594(5*n-3) = A017317(6*n-4) = A072710(4*n-2) = A139245(3*n-1). (End)

cp's OEIS Frontend

A105508 Numbers m such that 8 is the leading digit of the m-th Fibonacci number in decimal representation.

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions

A304158 a(n) is the second Zagreb index of the linear phenylene G[n], defined pictorially in the Darafsheh reference (Fig. 3).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Julia

Maple

PARI

PARI

Formula