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 A371000 #19 Apr 09 2025 15:13:30
%S A371000 0,1,3,6,9,12,15,21,27,33,45,87,99,102,123,156,246,273,282,330,429,
%T A371000 465,477,561,681,891,1050,1206,1338,1443,1449,1479,1656,1701,1836,
%U A371000 1899,1941,2151,2199,2280,2301,2517,2592,2595,2709,2724,2751,2760,2934,3045,3240,3333
%N A371000 a(n) are the records of the number of addends of the form j*(j+1)/2 (A000217) producing a sequence of consecutive composites starting at A370999(n).
%C A371000 The "Ponder This Challenge" of March 2024 asked for the smallest start value of sequences of at least 1000 (or 2024 to gain the bonus) composite numbers in a progression defined by A000217.
%H A371000 Karl-Heinz Hofmann and Hugo Pfoertner, <a href="/A371000/b371000.txt">Table of n, a(n) for n = 1..59</a>
%H A371000 IBM Research, <a href="https://research.ibm.com/haifa/ponderthis/challenges/March2024.html">Composite Sequences</a>, Ponder This Challenge March 2024.
%o A371000 (PARI) a371000(upto) = {my(m=0); forcomposite (k=4, upto, for (j=1, oo, if (isprime(k+(j*(j+1))/2), if (j>m, print1(j-1, ", "); m=j); break)))};
%o A371000 a371000(10^7)
%Y A371000 Cf. A000217, A370999, A371001, A371002.
%K A371000 nonn
%O A371000 1,3
%A A371000 _Karl-Heinz Hofmann_ and _Hugo Pfoertner_, Mar 09 2024