A117386 Positive integers, each occurring twice in the sequence, such that a(n) = a(k) when n+k = 6*a(n), starting with a(1)=1 and filling the next vacant position with the smallest unused number.

1, 2, 3, 4, 1, 5, 6, 7, 8, 2, 9, 10, 11, 12, 3, 13, 14, 15, 16, 4, 17, 18, 19, 5, 20, 21, 22, 23, 6, 24, 25, 26, 27, 7, 28, 29, 30, 31, 8, 32, 33, 34, 9, 35, 36, 37, 38, 10, 39, 40, 41, 42, 11, 43, 44, 45, 46, 12, 47, 48, 49, 13, 50, 51, 52, 53, 14, 54, 55, 56, 57, 15, 58, 59, 60, 61

Offset

1,2

Links

Table of n, a(n) for n=1..76.

Formula

a(6*a(n)-n) = a(n). Conjecture: Lim_inf a(n)/n = (3-sqrt(3))/6; Lim_sup a(n)/n = (3+sqrt(3))/6.

Prog

(PARI) {a(n)=local(A=vector(n), m=1); for(k=1, n, if(A[k]==0, A[k]=m; if(6*m-k<=#A, A[6*m-k]=m); m+=1)); A[n]}

Crossrefs

Cf. A117384 (a(4*a(n)-n)=a(n)), A117385 (a(5*a(n)-n)=a(n)).

Sequence in context: A104717 A067003 A277884 * A101174 A050144 A124406

Adjacent sequences: A117383 A117384 A117385 * A117387 A117388 A117389

Keyword

nonn

Author

Paul D. Hanna, Mar 11 2006

Status

approved