The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A117385 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing all changes.

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.
(history; published version)

#4 by Russ Cox at Fri Mar 30 18:36:56 EDT 2012

AUTHOR

_Paul D. Hanna (pauldhanna(AT)juno.com), _, Mar 11 2006

Discussion

Fri Mar 30

18:36

OEIS Server: https://oeis.org/edit/global/213

#3 by N. J. A. Sloane at Fri Feb 27 03:00:00 EST 2009

NAME

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.

KEYWORD

nonn,new

nonn

#2 by N. J. A. Sloane at Sat Nov 10 03:00:00 EST 2007

KEYWORD

nonn,new

nonn

AUTHOR

Paul D . Hanna (pauldhanna(AT)juno.com), Mar 11 2006

#1 by N. J. A. Sloane at Fri Feb 24 03:00:00 EST 2006

NAME

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.

DATA

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

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)).

KEYWORD

nonn

AUTHOR

Paul D Hanna (pauldhanna(AT)juno.com), Mar 11 2006

STATUS

approved