A117385 Positive integers, each occurring twice in the sequence, such that a(n) = a(k) when n+k = 5*a(n), starting with a(1)=1 and filling the next vacant position with the smallest unused number.

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

Offset

1,2

Links

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

Formula

a(5*a(n)-n) = a(n). Conjecture: Lim_inf a(n)/n = (5-sqrt(5))/10; Lim_sup a(n)/n = (5+sqrt(5))/10.

Prog

(PARI) {a(n)=local(A=vector(n), m=1); for(k=1, n, if(A[k]==0, A[k]=m; if(5*m-k<=#A, A[5*m-k]=m); m+=1)); A[n]}

Crossrefs

Cf. A117384 (a(4*a(n)-n)=a(n)), A117386 (a(6*a(n)-n)=a(n)).

Sequence in context: A122005 A362506 A306353 * A071517 A305433 A257681

Adjacent sequences: A117382 A117383 A117384 * A117386 A117387 A117388

Keyword

nonn

Author

Paul D. Hanna, Mar 11 2006

Status

approved