The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A083552 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A083552

Quotient when LCM of 2 consecutive prime differences is divided by GCD of the same two differences.
(history; published version)

#46 by Peter Luschny at Fri Apr 09 03:50:45 EDT 2021

STATUS

reviewed

approved

#45 by Joerg Arndt at Fri Apr 09 03:36:51 EDT 2021

STATUS

proposed

reviewed

#44 by Amiram Eldar at Fri Apr 09 03:29:46 EDT 2021

STATUS

editing

proposed

#43 by Amiram Eldar at Fri Apr 09 02:52:34 EDT 2021

MATHEMATICA

f[x_] := Prime[x+1]-Prime[x] ; Table[LCM[f[w+1], f[w]]/GCD[f[w+1], f[w]], {w, 1, 128}]

CROSSREFS

Cf. A001223, A083538..-A083555, A057467.

#42 by Amiram Eldar at Fri Apr 09 02:52:02 EDT 2021

LINKS

Amiram Eldar, <a href="/A083552/b083552.txt">Table of n, a(n) for n = 1..10000</a>

STATUS

approved

editing

#41 by N. J. A. Sloane at Mon Feb 11 19:44:52 EST 2019

STATUS

editing

approved

#40 by N. J. A. Sloane at Mon Feb 11 19:44:50 EST 2019

COMMENTS

Conjecture: Every positive integer appears infinitely many times in this sequence. ExamplesExample: a(834) = a(909) = ... = a(9901) = ... = 4; a(primepi(10^500+7137)) = 4396821. - Jerzy R Borysowicz, Dec 22 2018

STATUS

proposed

editing

#39 by Jerzy R Borysowicz at Tue Feb 05 12:49:02 EST 2019

STATUS

editing

proposed

Discussion

Tue Feb 05

22:23

Jon E. Schoenfield: Thanks!

Thu Feb 07

13:30

Michel Marcus: I don't see why this comment: a(primepi(10^500+7137)) = 4396821  ??

#38 by Jerzy R Borysowicz at Tue Feb 05 12:45:45 EST 2019

COMMENTS

All terms of this sequence are integers because because gcd(r,s) divide divides lcm(r,s) for any r and s. - Jerzy R Borysowicz, Jan 05 2019

Discussion

Tue Feb 05

12:48

Jerzy R Borysowicz: I have corrected see  #38 JB

#37 by Michel Marcus at Tue Feb 05 02:01:26 EST 2019

STATUS

proposed

editing