cp's OEIS Frontend

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.

A343239 Irregular triangle read by rows giving the solutions x for x^2 == -5 (mod A343238(n)), for x from {0, 1, 2, ..., A343238(n)-1}, for n >= 1.

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%I A343239 #19 Jan 06 2024 14:32:10
%S A343239 0,1,1,2,0,1,5,3,4,2,7,5,3,11,5,10,7,11,4,10,11,17,8,15,7,20,13,16,5,
%T A343239 25,10,25,6,35,11,17,25,31,9,34,20,25,15,31,18,29,17,32,7,47,13,45,19,
%U A343239 42,11,25,38,52,14,53,8,31,38,61,25,45,20,61,35,47,24,59,9,77,13,16,71,74
%N A343239 Irregular triangle read by rows giving the solutions x for x^2 == -5 (mod A343238(n)), for x from {0, 1, 2, ..., A343238(n)-1}, for n >= 1.
%C A343239 The length of row n is A343240(n).
%H A343239 Andrew Howroyd, <a href="/A343239/b343239.txt">Table of n, a(n) for n = 1..1468</a> (first 500 rows)
%F A343239 T(n, k) gives the solutions x from {0, 1, ..., A343238(n)-1} of the congruence x^2 + 5 == 0 (mod  A343238(n)), for n >= 1.
%e A343239 The irregular triangle T with A(n) = A343238(n) begins:
%e A343239    n  A(n) \ k  1  2  3  4 ...
%e A343239   ---------------------------
%e A343239    1,  1:       0
%e A343239    2,  2:       1
%e A343239    3,  3:       1  2
%e A343239    4,  5:       0
%e A343239    5,  6:       1  5
%e A343239    6,  7:       3  4
%e A343239    7,  9:       2  7
%e A343239    8, 10:       5
%e A343239    9, 14:       3 11
%e A343239   10, 15:       5 10
%e A343239   11, 18:       7 11
%e A343239   12, 21:       4 10 11 17
%e A343239   13, 23:       8 15
%e A343239   14, 27:       7 20
%e A343239   15, 29:      13 16
%e A343239   16, 30:       5 25
%e A343239   17, 35:      10 25
%e A343239   18, 41:       6 35
%e A343239   19, 42:      11 17 25 31
%e A343239   20, 43:       9 34
%e A343239   ...
%o A343239 (PARI) isok(k) = issquare(Mod(-5, k)); \\ A343238
%o A343239 lista(nn) = my(list = List()); for (n=1, nn, if (issquare(Mod(-5, n)), my(row = select(x->(Mod(x,n)^2 + 5 == 0), [0..n-1])); listput(list, row))); Vec(list); \\ _Michel Marcus_, Sep 17 2023
%Y A343239 Cf. A343238, A343240.
%K A343239 nonn,tabf,easy
%O A343239 1,4
%A A343239 _Wolfdieter Lang_, May 16 2021