A072682 -id:A072682 - cp's OEIS frontend

A105502 Numbers m such that 2 is the leading digit of the m-th Fibonacci number in decimal representation.

3, 8, 13, 18, 23, 32, 37, 42, 47, 51, 56, 61, 66, 75, 80, 85, 90, 99, 104, 109, 114, 118, 123, 128, 133, 142, 147, 152, 157, 166, 171, 176, 185, 190, 195, 200, 209, 214, 219, 224, 233, 238, 243, 252, 257, 262, 267, 276, 281, 286, 291, 295, 300, 305, 310, 319

Offset: 1

Reinhard Zumkeller, Apr 11 2005

A008963(a(n)) = 2; A105512(a(n)) = A105512(a(n) - 1) + 1.

			a(10)=51: A008963(51) = A000030(A000045(51)) = A000030(20365011074) = 2.

Winston de Greef, Table of n, a(n) for n = 1..10000

Cf. A000030, A000045, A072682, A105501, A105503, A105504, A105505, A105506, A105507, A105508, A105509.

Select[Range[400],First[IntegerDigits[Fibonacci[#]]]==2&] (* Harvey P. Dale, Jul 13 2015 *)

is(n)=digits(fibonacci(n))[1]==2 \\ Charles R Greathouse IV, Oct 07 2016

a(n) ~ kn by the equidistribution theorem, where k = log(10)/(log(3) - log(2)) = 5.67887.... - Charles R Greathouse IV, Oct 07 2016

A097022 a(n) = (sigma(2n^2)-3)/6.

Original entry on oeis.org

0, 2, 6, 10, 15, 32, 28, 42, 60, 77, 66, 136, 91, 142, 201, 170, 153, 302, 190, 325, 370, 332, 276, 552, 390, 457, 546, 598, 435, 1007, 496, 682, 864, 767, 883, 1270, 703, 952, 1189, 1317, 861, 1852, 946, 1396, 1875, 1382, 1128, 2216, 1400, 1952, 1995, 1921

Offset: 1

Labos Elemer, Aug 24 2004

nonn

See A065764, A065765 and A097022.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A065764, A065765, A000203, A001105, A002117, A072682, A074627, A074628, A074629, A074630, A067051.

Table[(DivisorSigma[1,2n^2]-3)/6,{n,60}] (* Harvey P. Dale, Sep 12 2022 *)

a(n) = (sigma(2*n^2) - 3)/6; \\ Michel Marcus, Dec 20 2013

a(n) = (A065765(n)-3)/6 = A000203(A001105(n) - 3)/6.

Sum_{k=1..n} a(k) ~ c * n^3, where c = 4*zeta(3)/Pi^2 = 0.243587... . - Amiram Eldar, Oct 28 2022

cp's OEIS Frontend

A105502 Numbers m such that 2 is the leading digit of the m-th Fibonacci number in decimal representation.

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