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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.
2
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
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
Sequence in context: A165160 A180411 A050436 * A214515 A270783 A330591
KEYWORD
easy,nonn,base
AUTHOR
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