The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A193558 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A193558

Differences between consecutive primes of the form k^2+1.
(history; published version)

#19 by Alois P. Heinz at Fri Dec 04 15:01:44 EST 2020

STATUS

proposed

approved

#18 by Michel Marcus at Fri Dec 04 12:20:13 EST 2020

STATUS

editing

proposed

#17 by Michel Marcus at Fri Dec 04 12:20:10 EST 2020

PROG

(PARI) lista(nn) = my(v=select(x->issquare(x-1), primes(nn))); vector(#v-1, k, v[k+1] - v[k]) \\ Michel Marcus, Dec 04 2020

STATUS

approved

editing

#16 by Joerg Arndt at Sun Nov 22 03:07:00 EST 2020

STATUS

reviewed

approved

#15 by Michel Marcus at Sun Nov 22 02:43:35 EST 2020

STATUS

proposed

reviewed

#14 by Amiram Eldar at Sun Nov 22 02:16:32 EST 2020

STATUS

editing

proposed

#13 by Amiram Eldar at Sun Nov 22 01:51:14 EST 2020

COMMENTS

It is conjectured that the sequence of primes of the form k^2+1 is infinite, but this has never been proved. This sequence contains a subset of squares: {64, 144, 100, 1024, 4900, 10816, 11664, 12544, 18496, 102400, 41616, ...}.

#12 by Amiram Eldar at Sun Nov 22 01:50:56 EST 2020

EXAMPLE

a(2) = 12 because (4^2+1)-(2^2+1) = 17 - 5 = 12.

#11 by Amiram Eldar at Sun Nov 22 01:50:37 EST 2020

LINKS

Amiram Eldar, <a href="/A193558/b193558.txt">Table of n, a(n) for n = 1..10000</a>

STATUS

approved

editing

#10 by Russ Cox at Fri Mar 30 18:35:58 EDT 2012

AUTHOR

_Michel Lagneau (mn.lagneau2(AT)orange.fr), _, Jul 30 2011

Discussion

Fri Mar 30

18:35

OEIS Server: https://oeis.org/edit/global/205