A038868 If a Fibonacci sequence is formed with first term = number of digits in n and second term = sum of decimal digits in n, then n itself occurs as a term in the sequence after the first two terms.
16, 21, 25, 50, 66, 102, 115, 154, 193, 291, 471, 573, 675, 777, 879, 2372, 3668, 4770, 6867, 22502, 22790, 32084, 41666, 46457, 167151, 331341, 490740, 1750051, 2125176, 2275226, 2425276, 2575326, 2725376, 2875426, 22597419, 73941113, 167637057, 188784525
Offset: 1
Examples
16 is a member because 2,7,9,16,25,... does contain 16.
Links
- Giovanni Resta, Table of n, a(n) for n = 1..1000
- Felice Russo, A Set of New Smarandache Functions, Sequences and Conjectures in Number Theory, Lupton, AZ: American Research Press, 2000.
Programs
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Mathematica
aQ[n_] := Module[{d = IntegerDigits[n], a}, a[1] = Length[d]; a[2] = Total[d]; a[k_] := a[k] = a[k - 1] + a[k - 2]; k = 1; While[a[k] <= n, k++]; k--; k > 2 && a[k] == n]; Select[Range[1000], aQ] (* Amiram Eldar, Feb 17 2019 *) gen[d_, s_, mx_] := Block[{a=d, b=s, v = {}, t}, While[True, t=a+b; If[t <= mx, If[d == IntegerLength@ t && s == Total@ IntegerDigits@ t, AppendTo[v, t]], Break[]]; a=b; b=t]; v]; upto[mxd_] := Sort@ Flatten@ Table[gen[d, s, 10^d], {d, mxd}, {s, 9*d}]; upto[20] (* terms < 10^20, Giovanni Resta, Feb 18 2019 *)
Extensions
Corrected and extended by Larry Reeves (larryr(AT)acm.org), Sep 28 2000
a(37)-a(38) from Amiram Eldar, Feb 17 2019
Comments