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Revision History for A245525

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A245525

Unique integer r with -prime(n)/2 < r <= prime(n)/2 such that p(n) == r (mod prime(n)), where p(.) is the partition function given by A000041.
(history; published version)

#22 by Max Alekseyev at Mon Jul 28 14:46:31 EDT 2014

STATUS

editing

approved

#21 by Max Alekseyev at Mon Jul 28 14:46:27 EDT 2014

COMMENTS

This conjecture does not hold with the smallest counterexample being n=1119414 (cf. A245662). - Max Alekseyev, Jul 27 2014

STATUS

approved

editing

#20 by Max Alekseyev at Sun Jul 27 16:00:15 EDT 2014

STATUS

editing

approved

#19 by Max Alekseyev at Sun Jul 27 16:00:09 EDT 2014

FORMULA

a(n) = A094252(n) or A094252(n)-A000040(n), depending on whether A094252(n) <= A000040(n)/2.

CROSSREFS

Cf. A000040, A000041, A094252, A245526.

STATUS

approved

editing

#18 by Max Alekseyev at Sun Jul 27 15:26:54 EDT 2014

STATUS

editing

approved

#17 by Max Alekseyev at Sun Jul 27 15:26:41 EDT 2014

COMMENTS

We have verified this for all n = 1, ..., 700000. Note that prime(700000) > 10^7.

This conjecture does not hold with the smallest counterexample being n=1119414. - Max Alekseyev, Jul 27 2014

STATUS

approved

editing

#16 by N. J. A. Sloane at Sat Jul 26 09:32:14 EDT 2014

STATUS

proposed

approved

#15 by Zhi-Wei Sun at Sat Jul 26 06:50:09 EDT 2014

STATUS

editing

proposed

#14 by Zhi-Wei Sun at Sat Jul 26 06:49:54 EDT 2014

COMMENTS

We have verified this for all n = 1, ..., 540000700000. Note that prime(700000) > 10^7.

STATUS

approved

editing

#13 by Michael Somos at Fri Jul 25 19:14:57 EDT 2014

STATUS

proposed

approved