The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A370600

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A370600

Numbers m such that 4m + k is squarefree for k = 1..3.
(history; published version)

#48 by Hugo Pfoertner at Tue Apr 16 03:06:32 EDT 2024

STATUS

reviewed

approved

#47 by Joerg Arndt at Tue Apr 16 02:40:38 EDT 2024

STATUS

proposed

reviewed

#46 by Amiram Eldar at Tue Apr 16 01:50:55 EDT 2024

STATUS

editing

proposed

#45 by Amiram Eldar at Tue Apr 16 01:42:11 EDT 2024

CROSSREFS

Cf. A005117, A007675, A008966, A206256, A258332.

#44 by Amiram Eldar at Tue Apr 16 01:41:51 EDT 2024

COMMENTS

The asymptotic density of this sequence is 4 * Product_{p prime} (1 - 3/p^2) = 4 * A206256 = 0.501947... . - Amiram Eldar, Apr 16 2024

PROG

(PARI) is(m) = issquarefree(4*m+1) && issquarefree(4*m+2) && issquarefree(4*m+3); \\ Amiram Eldar, Apr 16 2024

STATUS

approved

editing

#43 by OEIS Server at Mon Apr 15 18:10:45 EDT 2024

LINKS

Michael De Vlieger, <a href="/A370600/b370600_1.txt">Table of n, a(n) for n = 1..10000</a>

#42 by Hugo Pfoertner at Mon Apr 15 18:10:45 EDT 2024

STATUS

proposed

approved

Discussion

Mon Apr 15

18:10

OEIS Server: Installed first b-file as b370600.txt.

#41 by Michael De Vlieger at Mon Apr 15 14:58:04 EDT 2024

STATUS

editing

proposed

Discussion

Mon Apr 15

15:42

Hugo Pfoertner: It is well known that such questions only come from my automatic routine checking of new sequences with my extended search program. There are almost no mathematical considerations involved. But I pass on the information to the authors, as an editorial service, so to speak. If the relationship found is correct, then it can be used as a formula without my name.

15:43

Michael De Vlieger: Hugo, that is pretty handy! Thank you.

#40 by Michael De Vlieger at Mon Apr 15 14:57:02 EDT 2024

FORMULA

a(n) = (A007675(n)-1)/4.

STATUS

proposed

editing

Discussion

Mon Apr 15

14:58

Michael De Vlieger: Should attribute to Hugo if acceptable. Left off n > 1, since A7675(1) = 1, 1-1 = 0, and clearly {1, 2, 3} are squarefree.

#39 by Michael De Vlieger at Mon Apr 15 12:17:32 EDT 2024

STATUS

editing

proposed

Discussion

Mon Apr 15

13:26

Michel Marcus: add A007675 formula ??