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).

0, 1, 3, 6, 9, 12, 15, 21, 27, 33, 45, 87, 99, 102, 123, 156, 246, 273, 282, 330, 429, 465, 477, 561, 681, 891, 1050, 1206, 1338, 1443, 1449, 1479, 1656, 1701, 1836, 1899, 1941, 2151, 2199, 2280, 2301, 2517, 2592, 2595, 2709, 2724, 2751, 2760, 2934, 3045, 3240, 3333

Offset: 1

Author

Karl-Heinz Hofmann and Hugo Pfoertner, Mar 09 2024

Keywords

• nonn

Comments

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.

Links

• Karl-Heinz Hofmann and Hugo Pfoertner, Table of n, a(n) for n = 1..59
• IBM Research, Composite Sequences, Ponder This Challenge March 2024.

Crossrefs

Cf. A000217, A370999, A371001, A371002.

Programs

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)))};
a371000(10^7)