The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A073825

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A073825

Numbers n such that Sum_{k=1..n} k^k is prime.
(history; published version)

#38 by Joerg Arndt at Tue Feb 20 06:59:49 EST 2024

STATUS

editing

approved

#37 by Paolo P. Lava at Tue Feb 20 05:07:11 EST 2024

MAPLE

List073825:=proc(q) local a, n; a:=0;

for n from 1 to q do a:=a+n^n; if isprime(a) then print(n); fi; od; end:

List073825(100); # Paolo P. Lava, Apr 10 2013

STATUS

approved

editing

#36 by Sean A. Irvine at Sat Aug 08 18:15:24 EDT 2020

STATUS

proposed

approved

#35 by Michel Marcus at Tue Jul 21 01:16:52 EDT 2020

STATUS

editing

proposed

#34 by Michel Marcus at Tue Jul 21 01:16:40 EDT 2020

NAME

Numbers n such that Sum k^k, _{k=1..n, } k^k is prime.

PROG

(PARI) s=0; for(k=1, 1320, s=s+k^k; if(isprime(s), print1(k, ", ")))

#33 by Michel Marcus at Tue Jul 21 01:14:49 EDT 2020

LINKS

C. Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_404.htm">Puzzle 404. Sigma(x^x), for x=1 to n</a>, The Prime puzzle #404</a>Puzzles & Problems Connection.

STATUS

proposed

editing

#32 by Daniel Hoying at Mon Jul 20 13:58:38 EDT 2020

STATUS

editing

proposed

#31 by Daniel Hoying at Mon Jul 20 13:44:51 EDT 2020

COMMENTS

Conjecture: This sequence is infinite. - Daniel Hoying, Jul 20 2020

STATUS

approved

editing

Discussion

Mon Jul 20

13:58

Daniel Hoying: It appears Soundararajan already believed this to be true. The asymptotic probability of each successive term of A001923(n) being prime is ~1/(n log n) (by prime number theorem).  By https://en.wikipedia.org/wiki/Infinite_product, it follows that the prod (1-1/n log n) (the probability of all composite after a certain n) converges to a non-zero number iff. sum 1/n log n converges.  Since this sum diverges, we have confidence in the conjecture.

#30 by Bruno Berselli at Wed Mar 13 13:07:12 EDT 2019

STATUS

proposed

approved

#29 by Michel Marcus at Wed Mar 13 13:06:59 EDT 2019

STATUS

editing

proposed