The On-Line Encyclopedia of Integer Sequences (OEIS)

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A108541

Lesser prime factor of n-th golden semiprime.
(history; published version)

#9 by Bruno Berselli at Thu Nov 28 06:13:27 EST 2019

STATUS

proposed

approved

#8 by Amiram Eldar at Thu Nov 28 03:53:00 EST 2019

STATUS

editing

proposed

#7 by Amiram Eldar at Thu Nov 28 03:22:29 EST 2019

CROSSREFS

Cf. A001622, A084126, A108539, A108540, A108542, A108543, A108544, A108539.

#6 by Amiram Eldar at Thu Nov 28 03:21:31 EST 2019

COMMENTS

abs(phi*a(n) - A108542(n)/a(n)) < 1, where phi = golden ratio = (1+sqrt(5))/2.

#5 by Amiram Eldar at Thu Nov 28 03:20:03 EST 2019

COMMENTS

a(n) = A108540(n)/A108542(n);

FORMULA

a(n) = A108540(n)/A108542(n).

CROSSREFS

Cf. A001622, A084126, A108543, A108544, A108539.

#4 by Amiram Eldar at Thu Nov 28 03:18:46 EST 2019

LINKS

Amiram Eldar, <a href="/A108541/b108541.txt">Table of n, a(n) for n = 1..10000</a>

MATHEMATICA

f[p_] := Module[{x = GoldenRatio * p}, p1 = NextPrime[x, -1]; p2 = NextPrime[p1]; q = If[x - p1 < p2 - x, p1, p2]; If[Abs[q - x] < 1, q, 0]]; seq = {}; p=1; Do[p = NextPrime[p]; If[f[p] > 0, AppendTo[seq, p]], {200}]; seq (* Amiram Eldar, Nov 28 2019 *)

STATUS

approved

editing

#3 by Russ Cox at Fri Mar 30 18:50:50 EDT 2012

AUTHOR

_Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), _, Jun 09 2005

Discussion

Fri Mar 30

18:50

OEIS Server: https://oeis.org/edit/global/246

#2 by N. J. A. Sloane at Fri Jan 09 03:00:00 EST 2009

KEYWORD

nonn,new

nonn

AUTHOR

Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystemsgmail.com), Jun 09 2005

#1 by N. J. A. Sloane at Tue Jul 19 03:00:00 EDT 2005

NAME

Lesser prime factor of n-th golden semiprime.

DATA

2, 3, 7, 11, 19, 23, 29, 37, 41, 67, 79, 97, 101, 103, 107, 131, 149, 163, 167, 181, 193, 227, 241, 271, 277, 283, 311, 353, 367, 379, 383, 397, 409, 419, 433, 449, 457, 487, 509, 563, 607, 613, 631, 661, 719, 733, 761, 797, 853, 883, 919, 941, 971, 997, 1031

OFFSET

1,1

COMMENTS

a(n) = A108540(n)/A108542(n);

abs(phi-A108542(n)/a(n)) < 1, where phi = golden ratio = (1+sqrt(5))/2.

CROSSREFS

Cf. A084126, A108543, A108544, A108539.

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Jun 09 2005

STATUS

approved