A053049 -id:A053049 - cp's OEIS frontend

A053056 Fibonacci numbers whose digit sum is also a Fibonacci number.

0, 1, 2, 3, 5, 8, 21, 233, 317811, 3524578, 7778742049, 259695496911122585, 19740274219868223167, 10284720757613717413913, 263621064469290555679241849789653324393054271110084140201023

Offset: 1

Felice Russo, Feb 25 2000

Is this sequence finite?

It is heuristically infinite because of the divergence of the harmonic series. - Charles R Greathouse IV, Sep 20 2012

			317811 is in the sequence because the sum of its digits 3+1+7+8+1+1=21 is also a Fibonacci number. - Luc Stevens (lms022(AT)yahoo.com), Apr 15 2006

Chai Wah Wu, Table of n, a(n) for n = 1..24 (all terms < 10^1000).
Felice Russo, A set of new Smarandache functions, sequences and conjectures in number theory.

Cf. A000045, A053056, A061268, A053049.

with(combinat): F:=[seq(fibonacci(n),n=2..80)]: a:=proc(n) local ff, sod: ff:=convert(fibonacci(n), base,10): sod:=add(ff[i],i=1..nops(ff)): if member(sod,F)=true then fibonacci(n) else fi end: seq(a(n),n=2..300); # Emeric Deutsch, Apr 17 2006

More terms from Larry Reeves (larryr(AT)acm.org), Oct 03 2000
More terms from Emeric Deutsch, Apr 17 2006
Edited by R. J. Mathar, Aug 08 2008

A306762 Smallest integer k such that Sum_(i=1..k) lambda(i) is divisible by n, where lambda(i) is the Carmichael lambda function.

Original entry on oeis.org

1, 2, 4, 3, 5, 4, 12, 11, 7, 5, 49, 6, 9, 12, 10, 15, 16, 7, 24, 8, 12, 49, 26, 30, 23, 9, 13, 17, 55, 10, 58, 15, 71, 16, 44, 19, 169, 24, 100, 11, 48, 12, 25, 49, 18, 26, 38, 30, 40, 23, 164, 28, 50, 13, 141, 20, 47, 55, 21, 14, 80, 58, 192, 15, 110, 71, 76

Offset: 1

Michel Lagneau, Mar 08 2019

			a(7) = 12 because Sum_{i=1..12} lambda(i) = 1 + 1 + 2 + 2 + 4 + 2 + 6 + 2 + 6 + 4 + 10 + 2 = 42, and 42/7 = 6.

Cf. A002322 (Carmichael lambda), A162578 (partial sums of A002322).

Cf. A053049 (analog with totient function).

S:= ListTools:-PartialSums(map(numtheory:-lambda, [$1..500])):
N:= 100: count:= 0: V:= Vector(N):
for n from 1 to 500 while count < N do
   d:= select(t -> t <= N and V[t] = 0, numtheory:-divisors(S[n]));
   count:= count + nops(d);
   V[convert(d,list)]:= n;
od:
convert(V,list); # Robert Israel, Mar 11 2019

a[n_] := (m = 1; While[! IntegerQ[Sum[CarmichaelLambda[k], {k, 1, m}]/n], m++]; m); a /@ Range[80]

lambda(n) = lcm(znstar(n)[2]);
a(n) = {my(k=1, s=lambda(k)); while (s % n, k++; s += lambda(k)); k;} \\ Michel Marcus, Mar 09 2019

cp's OEIS Frontend

A053056 Fibonacci numbers whose digit sum is also a Fibonacci number.

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