A107436 a(n) = (a^5)(n-1) + a(n-a(n-1)) = a(a(a(a(a(n-1))))) + a(n-a(n-1)), a(1) = a(2) = 1.

1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13

Offset

1,3

Comments

Multi-recursive sequence suggested by A004001: 5th level.

If A004001 is a level 2 recursion, A087817 is a level 3, and A087836 is a level 4, then this sequence is the 5th level. Other multi-recursives approximate this sequence for initial terms: A087845, A087847 Benoit Cloitre's sequence is: d = Table[Ceiling[n^.56], {n, 1, digits}].

Satisfies a(n) = A002024(n-1) up to n=2280, but is strictly larger thereafter. The graph shows an interesting "phase break" (author's terms in A087836) just after 2281. Are there other such "irregularities" to be expected (when a(n) attains 2281, or later)? - M. F. Hasler, Apr 20 2014

Links

M. F. Hasler, Table of n, a(n) for n = 1..10000

Example

From n=2 to n=2280, a(n)=A002024(n-1); in particular, a(2280)=68 is preceded by 67 copies of 67. But a(2281) = a(a(a(a(a(2280))))) + a(2281-a(2280)) = a(a(a(a(68)))) + a(2281-68) = a(a(a(12))) + a(2213) = a(a(5)) + 67 =69. - M. F. Hasler, Apr 21 2014

Maple

a := proc(n) option remember; `if`(n<3, 1, (a@@(5))(n-1)+a(n-a(n-1))) end; # Peter Luschny, Apr 23 2014

Mathematica

a[1] = a[2] = 1; a[n_Integer?Positive] := a[n] = Nest[a, n-1, 5] + a[n - a[n - 1]]; Table[a[n], {n, 1, 255}]

Prog

(PARI) a107436=[1, 1]; A107436(n)={if(n>#a107436, a107436=concat(a107436, vector(n-#a107436)), a107436[n] && return(a107436[n])); t=A107436(n-1); a107436[n]=A107436(n-t)+A107436(A107436(A107436(A107436(t))))} \\ M. F. Hasler, Apr 21 2014

Crossrefs

Cf. A028310, A004001, A087817, A087836, A087845, A087847.

Sequence in context: A274094 A274093 A087847 * A002024 A123578 A087836

Adjacent sequences: A107433 A107434 A107435 * A107437 A107438 A107439

Keyword

nonn

Author

Roger L. Bagula, May 26 2005

Status

approved