A228297 Generalized meta-Fibonacci sequence a(n) with parameters s=0 and k=5.

1, 2, 3, 4, 5, 5, 6, 7, 8, 9, 10, 10, 11, 12, 13, 14, 15, 15, 16, 17, 18, 19, 20, 20, 21, 22, 23, 24, 25, 25, 25, 26, 27, 28, 29, 30, 30, 31, 32, 33, 34, 35, 35, 36, 37, 38, 39, 40, 40, 41, 42, 43, 44, 45, 45, 46, 47, 48, 49, 50, 50, 50, 51, 52, 53

Offset: 1

Author

Michel Marcus, Aug 20 2013

Keywords

• nonn

Comments

Each integer n appears x+1 times where x is the greatest power of 5 in the factorization of n!. - Gerald Hillier, Feb 08 2020

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000
• C. Deugau and F. Ruskey, Complete k-ary Trees and Generalized Meta-Fibonacci Sequences, J. Integer Seq., Vol. 12, 2009, Article 09.4.3.

Crossrefs

Cf. A120503, A120507, A228298.

Programs

Mathematica

Array[ConstantArray[#, IntegerExponent[#, 5] + 1] &, 53] // Flatten (* Michael De Vlieger, Feb 08 2020 *)

PARI

a(n)= {local(A); if(n<=5, max(0, n), A=vector(n, i, i); for(k=6, n, A[k]= A[k-A[k-1]] + A[k-1-A[k-2]] + A[k-2-A[k-3]] + A[k-3-A[k-4]] + A[k-4-A[k-5]];); A[n];);}
(HP 49G calculator)
« DUPDUP 5 IQUOT -
  WHILE DUP 0 OVER
    DO 5 IQUOT DUP
ROT + SWAP DUP NOT
    UNTIL
    END DROP +
PICK3 <
  REPEAT 1 +
  END NIP
» Gerald Hillier, Sep 19 2017

Formula

a(n) = A007845(n)/5. - M. F. Hasler, Dec 27 2019