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
Keywords
Programs
-
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]}
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.