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Revision History for A203464

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A203464

Numbers n such that 65 divides 4n^2 + 1; alternately, numbers which are 4, 9, 56, or 61 mod 65.
(history; published version)

#60 by Michael De Vlieger at Thu Mar 16 08:50:19 EDT 2023

STATUS

reviewed

approved

#59 by Amiram Eldar at Thu Mar 16 08:06:51 EDT 2023

STATUS

proposed

reviewed

#58 by Michel Marcus at Thu Mar 16 07:14:32 EDT 2023

STATUS

editing

proposed

#57 by Michel Marcus at Thu Mar 16 07:14:25 EDT 2023

LINKS

W. Sierpiński, <a href="httphttps://www.isinj.com/aimemt-usamo/250%20Problems%20in%20Elementary%20Number%20Theory%20-%20Sierpinski%20%281970%29(1970).pdf">250 Problems in Elementary Number Theory</a>, (Modern Analytic and Computational Methods in Science and Mathematics, No. 26), American Elsevier Publishing Co., Inc., New York; PWN Polish Scientific Publishers, Warsaw, 1970, pp. 1, 23.

<a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).

PROG

(Maxima) makelist((1/8)*(130*n+78*%i^(n*(n+1))-45*(-1)^n-65), n, 1, 53); [_/* _Bruno Berselli_, Jan 12 2012] */

STATUS

approved

editing

#56 by Charles R Greathouse IV at Thu Sep 08 08:46:01 EDT 2022

PROG

(MAGMAMagma) m:=54; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(x*(4+5*x+47*x^2+5*x^3+4*x^4)/((1-x)^2*(1+x+x^2+x^3)))); // Bruno Berselli, Jan 12 2012

Discussion

Thu Sep 08

08:46

OEIS Server: https://oeis.org/edit/global/2944

#55 by Wolfdieter Lang at Tue Oct 13 13:42:44 EDT 2015

STATUS

editing

approved

#54 by Wolfdieter Lang at Tue Oct 13 13:42:24 EDT 2015

LINKS

Waclaw W. Sierpiński, <a href="http://www.isinj.com/aime/250%20Problems%20in%20Elementary%20Number%20Theory%20-%20Sierpinski%20%281970%29.pdf">250 Problems in Elementary Number Theory</a>, (Modern Analytic and Computational Methods in Science and Mathematics, No. 26), American Elsevier Publishing Co., Inc., New York; PWN Polish Scientific Publishers, Warsaw, 1970, pp. 1, 23.

STATUS

proposed

editing

#53 by Danny Rorabaugh at Tue Oct 13 12:31:41 EDT 2015

STATUS

editing

proposed

Discussion

Tue Oct 13

13:41

Wolfdieter Lang: In the link (translation) it is W.  Sierpiński (I checked the book).

13:48

Robert Israel: We tend to use initials rather than first names in references and links to published literature.  Also I think we want to avoid non-ASCII characters if at all possible: some users' systems may have trouble with characters such as "ń" So I'd go with W. Sierpinski.

#52 by Danny Rorabaugh at Tue Oct 13 12:30:23 EDT 2015

REFERENCES

Waclaw Sierpinski, Wacław Sierpiński, 200 zadan z elementarnej teorii liczb, Warsaw: PZWS, 1964, pp. 5, 29.

Sierpinski, W., 250 Problems in Elementary Number Theory. (Modern Analytic and Computational Methods in Science and Mathematics, No. 26), American Elsevier Publishing Co., Inc., New York; PWN Polish Scientific Publishers, Warsaw, 1970, pp. 1, 23.

LINKS

Waclaw Sierpiński, <a href="http://www.isinj.com/aime/250%20Problems%20in%20Elementary%20Number%20Theory%20-%20Sierpinski%20%281970%29.pdf">250 Problems in Elementary Number Theory</a>, (Modern Analytic and Computational Methods in Science and Mathematics, No. 26), American Elsevier Publishing Co., Inc., New York; PWN Polish Scientific Publishers, Warsaw, 1970, pp. 1, 23.

STATUS

approved

editing

Discussion

Tue Oct 13

12:31

Danny Rorabaugh: His name is Waclaw instead of Wacław in the translated work. Should that link then be "W. Sierpiński", "Waclaw Sierpiński", or "Wacław Sierpiński"?

#51 by Charles R Greathouse IV at Sat Jun 13 00:54:09 EDT 2015

LINKS

<a href="/index/Rec">Index to sequences with entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).

Discussion

Sat Jun 13

00:54

OEIS Server: https://oeis.org/edit/global/2439