The On-Line Encyclopedia of Integer Sequences (OEIS)

Revisions by Jonathan Sondow (See also Jonathan Sondow's wiki page)

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A309132

a(n) is the denominator of F(n) = A027641(n-1)/n + A027642(n-1)/n^2.
(history; published version)

#106 by Jonathan Sondow at Fri Aug 16 19:26:54 EDT 2019

STATUS

editing

proposed

#105 by Jonathan Sondow at Fri Aug 16 19:26:42 EDT 2019

COMMENTS

The values of F(n) when n is prime are A327033. - Jonathan Sondow, Aug 16 2019

CROSSREFS

Cf. A000040, A000146, A002997, A027641, A027642, A110936, A166062, A174341, A174342, A309235, A326690, A327033.

STATUS

approved

editing

A174341

a(n) = numerator(Bernoulli(n, 1) + 1/(n+1)).
(history; published version)

#50 by Jonathan Sondow at Fri Aug 16 19:23:20 EDT 2019

STATUS

editing

proposed

#49 by Jonathan Sondow at Fri Aug 16 19:23:07 EDT 2019

COMMENTS

The "if" part of the conjecture is true: see the theorems in A309132 and A326690. The values of the numerator when n+1 is prime are A327033. - Jonathan Sondow, Aug 15 2019

CROSSREFS

Cf. A164555, A027642, A174342 (denominators), A025529, A003506, A309132, A326690, A327033.

STATUS

approved

editing

A327033

N(p-1)/p + D(p-1)/p^2 with p the n-th prime and B(k) = N(k)/D(k) the k-th Bernoulli number.
(history; published version)

#5 by Jonathan Sondow at Thu Aug 15 19:58:44 EDT 2019

STATUS

editing

proposed

#4 by Jonathan Sondow at Thu Aug 15 19:57:39 EDT 2019

LINKS

Wikipedia, <a href="https://en.wikipedia.org/wiki/Bernoulli_number">Bernoulli number</a>

EXAMPLE

Prime(6) = 13 and B(12) = -691/2730, so a(6) = -691/13 + 2730/13^2 = -37.

#3 by Jonathan Sondow at Thu Aug 15 19:49:39 EDT 2019

NAME

allocated for Jonathan SondowN(p-1)/p + D(p-1)/p^2 with p the n-th prime and B(k) = N(k)/D(k) the k-th Bernoulli number.

DATA

0, 1, 1, 1, 1, -37, -211, 2311, 37153, -818946931, 277930363757, -711223555487930419, -6367871182840222481, 35351107998094669831, 12690449182849194963361, -15116334304443206742413679091, 1431925649981017658678758915153153, -19921854762028779869513196624259348280501

OFFSET

1,6

COMMENTS

a(n) is an integer, as conjectured by Thomas Ordowski and proved by the author in A309132 and A326690.

Ordowski also conjectured that the sequence is a subsequence of A174341.

EXAMPLE

Prime(6) = 13 and B(12) = -691/2730

MATHEMATICA

a[n_] := With[{p = Prime[n]}, With[{b = BernoulliB[p - 1]}, (p Numerator[b] + Denominator[b])/p^2]];

Table[a[n], {n, 1, 18}]

CROSSREFS

Cf. A174341, A309132, A326690.

KEYWORD

allocated

sign

AUTHOR

Jonathan Sondow, Aug 15 2019

STATUS

approved

editing

#2 by Jonathan Sondow at Thu Aug 15 19:02:59 EDT 2019

KEYWORD

allocating

allocated

A327034

Expansion of e.g.f. exp(x) / (2 - cosh(x)).
(history; published version)

#1 by Jonathan Sondow at Thu Aug 15 19:02:59 EDT 2019

NAME

allocated for Jonathan Sondow

KEYWORD

allocated

STATUS

approved

A327035

An unbounded sequence consisting solely of Fibonacci numbers with the property that for any four consecutive terms the maximum term is the sum of the two minimum terms.
(history; published version)

#1 by Jonathan Sondow at Thu Aug 15 19:02:59 EDT 2019

NAME

allocated for Jonathan Sondow

KEYWORD

allocated

STATUS

approved