The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A111002 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A111002

a(n) = gcd(f(n), f(n+1)) where f(n) = n^4 + n^2 + 1.
(history; published version)

#26 by Charles R Greathouse IV at Thu Sep 08 08:45:20 EDT 2022

PROG

(MAGMAMagma) [Gcd(n^4+n^2+1, n^4+4*n^3+7*n^2+6*n+3): n in [0..50]]; // Vincenzo Librandi, Oct 07 2015

Discussion

Thu Sep 08

08:45

OEIS Server: https://oeis.org/edit/global/2944

#25 by Michel Marcus at Wed Oct 07 09:36:47 EDT 2015

STATUS

reviewed

approved

#24 by Joerg Arndt at Wed Oct 07 08:52:04 EDT 2015

STATUS

proposed

reviewed

#23 by Vincenzo Librandi at Wed Oct 07 01:52:30 EDT 2015

STATUS

editing

proposed

#22 by Vincenzo Librandi at Wed Oct 07 01:52:08 EDT 2015

PROG

(MAGMA) [Gcd(n^4+n^2+1, n^4+4*n^3+7*n^2+6*n+3): n in [0..50]]; // Vincenzo Librandi, Oct 07 2015

STATUS

proposed

editing

#21 by Jon E. Schoenfield at Tue Oct 06 21:05:46 EDT 2015

STATUS

editing

proposed

#20 by Jon E. Schoenfield at Tue Oct 06 21:05:44 EDT 2015

NAME

a(n) = gcd( f(n), f(n+1)) where f(n) = n^4 + n^2 + 1.

FORMULA

a(n) = gcd(f(n), f(n+1)) for all n. a(n) = n^2 + n + 1, except when n congruent to 3 modulo 7 when a(n) = 7(n^2 + n + 1).

EXAMPLE

a(10) = 7(10^2 + 10 + 1) = 777 because 10 is congruent to 3 modulo 7.

STATUS

proposed

editing

#19 by Michel Marcus at Tue Oct 06 05:41:19 EDT 2015

STATUS

editing

proposed

#18 by Michel Marcus at Tue Oct 06 05:39:53 EDT 2015

MATHEMATICA

f[n_] := n^4 + n^2 + 1; Table[ GCD[f[n], f[n + 1]], {n, 0, 49}] (* Robert G. Wilson v , Oct 02 2005 *)

PROG

(PARI) m=50; a=3; for(k=2, m, b=k^4+k^2+1; print1(gcd(a, b), ", "); a=b) \\ Klaus Brockhaus, Oct 02 2005

STATUS

proposed

editing

Discussion

Tue Oct 06

05:41

Michel Marcus: yes, thanks

#17 by Colin Barker at Tue Oct 06 05:32:17 EDT 2015

STATUS

editing

proposed