This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A256101 #29 Nov 13 2024 05:38:05
%S A256101 301,721,1141,1561,1981,2401,2821,3241,3661,4081,4501,4921,5341,5761,
%T A256101 6181,6601,7021,7441,7861,8281,8701,9121,9541,9961,10381,10801,11221,
%U A256101 11641,12061,12481,12901,13321,13741,14161,14581,15001,15421,15841
%N A256101 The broken eggs problem.
%C A256101 This is a problem of byzantine mathematics appearing in the Codex Vinobonensis Phil. Gr. 65. See the Hunger-Vogel reference, p. 73, problem 86.
%C A256101 It also appears in the Tropfke reference on p. 640, 4.3.5.2, Die Eierfrau, as a special case of the Chinese Ta-yen rule (method of the great extension) treated on p. 636.
%C A256101 This is also a problem posed in the Alten et al. reference, p. 203, Aufgabe 3.1.6 (taken from Tropfke).
%C A256101 For the statement of the problem (in another setting) see the Cherowitzo link, where it is considered as an application of the Chinese remainder theorem.
%C A256101 The problem is to find all solutions of the common congruences: N congruent to 1 modulo 2, 3, 4, 5 and 6, and 0 modulo 7. For the application of the Chinese remainder theorem one first disposes of the moduli 2 and 6 (these congruences follow from the others).
%C A256101 The egg-selling woman had 301 eggs before they were broken according to problem 86 with this special solution in the Hunger-Vogel reference.
%D A256101 H.-W. Alten et al., 4000 Jahre Algebra, 2. Auflage, Springer, 2014, p. 203.
%D A256101 H. Hunger and K. Vogel, Ein byzantinisches Rechenbuch des 15.Jahrhunderts. 100 Aufgaben aus dem Codex Vindobonensis Phil. Gr. 65. (in Greek and German translation), Hermann Böhlaus Nachf., Wien, 1963 (Österr. Akad. d. Wiss., phil.-hist. Kl., Denkschriften, 78. Band, 2. Abhandlung), p. 73.
%D A256101 J. Tropfke, Geschichte der Elementarmathematik, Band 1, Arithmetik und Algebra, 4. Auflage, Walter de Gruyter, Berlin, New York , 1980, p. 640.
%H A256101 Adam Hugill, <a href="/A256101/b256101.txt">Table of n, a(n) for n = 1..10000</a>
%H A256101 Bill Cherowitzo, <a href="http://www-math.ucdenver.edu/~wcherowi/courses/m5410/crt.pdf">Chinese remainder Theorem</a>.
%H A256101 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2, -1).
%F A256101 a(n) = 420*n-119, n >= 1, (note that 420 = 3*4*5*7, with pairwise coprime factors needed for the Chinese remainder theorem).
%F A256101 a(n) = 60*A017041(n-1) + 1, n >= 1.
%F A256101 G.f.: x*7*(43+17*x)/(1-x)^2. [Corrected by _Vincenzo Librandi_, Apr 11 2015]
%p A256101 A256101:=n->420*n-119: seq(A256101(n), n=1..50); # _Wesley Ivan Hurt_, Apr 11 2015
%t A256101 CoefficientList[Series[(301 + 119 x) / (1 - x)^2, {x, 0, 40}], x] (* _Vincenzo Librandi_, Apr 11 2015 *)
%o A256101 (Magma) [420*n-119: n in [1..40]]; // _Vincenzo Librandi_, Apr 11 2015
%o A256101 (Python)
%o A256101 terms=[]
%o A256101 n=50 #terms here
%o A256101 for i in range(1, n+1):
%o A256101 ans=420*i-119
%o A256101 terms.append(ans)
%o A256101 print(terms)
%o A256101 # _Adam Hugill_, Feb 22 2022
%Y A256101 Cf. A017041.
%K A256101 nonn,easy
%O A256101 1,1
%A A256101 _Wolfdieter Lang_, Apr 10 2015
%E A256101 Corrected G.f. rewritten. - _Wolfdieter Lang_, Apr 15 2015