A220989 -id:A220989 - cp's OEIS frontend

A220990 a(n) = 12^(2n+1) + 6 * 12^n + 1: the right Aurifeuillian factor of 12^(6n+3) + 1.

19, 1801, 249697, 35842177, 5159904769, 743009863681, 106993223294977, 15407021789577217, 2218611109320327169, 319479999401581608961, 46005119909741205651457, 6624737266953695061344257, 953962166440743626203987969

Offset: 0

Stuart Clary, Dec 27 2012

The corresponding left Aurifeuillian factor is A220989.

Wikipedia, Cunningham Project
Index entries for linear recurrences with constant coefficients, signature (157,-1884,1728).

Cf. A092440, A085601, A220978, A198410, A220979-A220989.

Table[12^(2n+1) + 6 * 12^n + 1, {n, 0, 10}]
LinearRecurrence[{157,-1884,1728},{19,1801,249697},20] (* Harvey P. Dale, Mar 26 2022 *)

a(n)=12^(2*n+1)+6*12^n+1 \\ Charles R Greathouse IV, Sep 28 2015

Aurifeuillian factorization: 12^(6n+3) + 1 = (12^(2n+1) + 1) * A220989(n) * a(n).

G.f.: -(2736*x^2-1182*x+19) / ((x-1)*(12*x-1)*(144*x-1)). - Colin Barker, Jan 03 2013

A220986 The right Aurifeuillian factor of 10^(20n + 10) + 1.

Original entry on oeis.org

27961, 1105207205101, 101005020070200501001, 10010005002000700200050010001, 1000100005000200007000200005000100001, 100001000005000020000070000200000500001000001, 10000010000005000002000000700000200000050000010000001

Offset: 0

Stuart Clary, Dec 27 2012

The corresponding left Aurifeuillian factor is A220985.

Wikipedia, Cunningham Project

Cf. A092440, A085601, A220978, A198410, A220979, A220980, A220981, A220982

Cf. A220983, A220984, A220985, A220987, A220988, A220989, A220990

a[n_] := 10^(8n + 4) + 10^(7n + 4) + 5 * 10^(6n + 3) + 2 * 10^(5n + 3) + 7 * 10^(4n + 2) + 2 * 10^(3n + 2) + 5 * 10^(2n + 1) + 10^(n + 1) + 1

a(n) = 10^(8n + 4) + 10^(7n + 4) + 5 * 10^(6n + 3) + 2 * 10^(5n + 3) + 7 * 10^(4n + 2) + 2 * 10^(3n + 2) + 5 * 10^(2n + 1) + 10^(n + 1) + 1

Aurifeuillian factorization: 10^(20n + 10) + 1 = (10^(4n + 2) + 1) * A220985(n) * a(n)

cp's OEIS Frontend

A220990 a(n) = 12^(2n+1) + 6 * 12^n + 1: the right Aurifeuillian factor of 12^(6n+3) + 1.

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