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

1,1

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.

Example

16 is a member because 2,7,9,16,25,... does contain 16.

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 *)

Crossrefs

Cf. A007629, A042983.

Sequence in context: A165160 A180411 A050436 * A214515 A270783 A330591

Adjacent sequences: A038865 A038866 A038867 * A038869 A038870 A038871

Keyword

easy,nonn,base

Author

Felice Russo

Extensions

Corrected and extended by Larry Reeves (larryr(AT)acm.org), Sep 28 2000

a(37)-a(38) from Amiram Eldar, Feb 17 2019

Status

approved