

A079051


Recamán variation: a(0) = 0; for n >= 1, a(n) = a(n1)  f(n) if that number is positive and not already in the sequence, otherwise a(n) = a(n1) + f(n), where f(n) = floor(sqrt(n)) (A000196).


7



0, 1, 2, 3, 5, 7, 9, 11, 13, 10, 13, 16, 19, 22, 25, 28, 24, 20, 24, 28, 32, 36, 40, 44, 48, 43, 38, 33, 38, 43, 48, 53, 58, 63, 68, 73, 67, 61, 55, 49, 55, 61, 67, 73, 79, 85, 91, 97, 103, 96, 89, 82, 75, 82, 89, 96, 103, 110, 117, 124, 131, 138, 145, 152, 144, 136, 128, 120
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OFFSET

0,3


REFERENCES

N. J. A. Sloane and Allan Wilks, On sequences of Recaman type, paper in preparation, 2006.


LINKS

Ivan Neretin, Table of n, a(n) for n = 0..10000
Nick Hobson, Python program for this sequence


FORMULA

Conjecture: for n>100, 1/2 < a(n)/(n*log(n)) < 1.
The conjecture is false. In fact, a(n) = n^(3/2)/6 + O(n).  N. J. A. Sloane, Apr 29 2006


MATHEMATICA

Fold[Append[#1, If[MemberQ[#1, (a = #1[[1]])  (r = Floor@Sqrt@#2)], a + r, a  r]] &, {0, 1}, Range[2, 70]] (* Ivan Neretin, Apr 22 2018 *)


PROG

(PARI) lista(nn) = {va = vector(nn+1); last = 0; for (n=1, nn, new = last  sqrtint(n); if ((new <= 0)  vecsearch(vecsort(va, , 8), new), new = last + sqrtint(n)); va[n+1] = new; last = new; ); va; } \\ Michel Marcus, Apr 23 2018


CROSSREFS

Cf. A000196, A005132. Numbers missed are in A117247.
Cf. A117248, A117516, A117518.
Sequence in context: A186290 A061979 A050748 * A226047 A066935 A042943
Adjacent sequences: A079048 A079049 A079050 * A079052 A079053 A079054


KEYWORD

nonn


AUTHOR

Benoit Cloitre, Feb 02 2003


STATUS

approved



