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, 3546, 3576, 3867, 3984

Offset

1,3

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

Table of n, a(n) for n=1..56.

IBM Research, Composite Sequences, Ponder This Challenge March 2024.

Prog

(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)

Crossrefs

Cf. A000217, A370999, A371001, A371002.

Sequence in context: A194273 A123581 A187337 * A184999 A289761 A310151

Adjacent sequences: A370997 A370998 A370999 * A371001 A371002 A371003

Keyword

nonn

Author

Karl-Heinz Hofmann and Hugo Pfoertner, Mar 09 2024

Status

approved