The On-Line Encyclopedia of Integer Sequences® (OEIS®)

Revision History for A245634

(Underlined text is an addition; strikethrough text is a ~~deletion~~.)
Showing all changes.

A245634

Least number k such that (n^k-k^n)/(k-n) is prime, or 0 if no such number exists.
(history; published version)

#6 by N. J. A. Sloane at Tue Jul 29 21:04:17 EDT 2014

STATUS

proposed

approved

#5 by Derek Orr at Mon Jul 28 00:13:03 EDT 2014

STATUS

editing

proposed

#4 by Derek Orr at Mon Jul 28 00:13:00 EDT 2014

CROSSREFS

#3 by Derek Orr at Mon Jul 28 00:11:23 EDT 2014

PROG

a(n)=for(k=1, 10^34, if(k!=n, s=(n^k-k^n)/(k-n); if(floor(s)==s, if(ispseudoprime(s), return(k)))))

#2 by Derek Orr at Mon Jul 28 00:10:59 EDT 2014

	NAME	`allocatedLeast number k such that (n^k-k^n)/(k-n) is prime, or 0 if no forsuch Dereknumber Orrexists.`
	DATA	`0, 6, 4, 3, 3, 2, 3, 0, 5, 7, 3, 13, 11, 0, 17, 0, 15, 0, 7, 0, 0, 15, 5, 0, 79, 0, 0, 0, 15, 0, 0, 0, 65, 0, 47, 0, 39, 0, 37, 0, 9, 0, 0, 45, 44, 0, 11, 0, 103, 0, 71, 0, 11, 0, 119, 0, 5, 0, 0, 0, 0, 0, 0, 0, 33, 0, 75, 0, 77, 0, 51, 143, 0, 0, 67, 0, 69, 0, 25, 0, 131, 0, 0, 0, 57, 0, 8887, 0, 221, 0, 291, 0, 0, 0, 0, 0, 101, 0, 0`
	OFFSET	`1,2`
	COMMENTS	`a(1) = 0 is the only confirmed 0 in this sequence.` `a(n) = 0 for n > 1 is confirmed for k < 10000.` `If a(n) = m, then a(m) <= n for m > 0 and n > 0.`
	EXAMPLE	`(2^1-1^2)/(1-2) = -1 is not prime.` `(2^3-3^2)/(3-2) = -1 is not prime.` `(2^4-4^2)/(4-2) = 0 is not prime.` `(2^5-5^2)/(5-2) = 7/3 is not prime.` `(2^6-6^2)/(6-2) = 7 is prime. Thus a(2) = 6.`
	PROG	`(PARI)` `a(n)=for(k=1, 10^3, if(k!=n, s=(n^k-k^n)/(k-n); if(floor(s)==s, if(ispseudoprime(s), return(k)))))` `n=1; while(n<100, print1(a(n), ", "); n++)`
	KEYWORD	`allocated` `nonn`
	AUTHOR	`Derek Orr, Jul 28 2014`
	STATUS	`approved` `editing`

#1 by Derek Orr at Mon Jul 28 00:10:59 EDT 2014

Last modified July 24 12:16 EDT 2024. Contains 374583 sequences. (Running on oeis4.)