A371002 -id:A371002 - cp's OEIS frontend

A371001 Least number k such that the number m of consecutive composite sums k + j^2, j = 0, ..., m is a new maximum.

4, 8, 21, 24, 26, 119, 134, 185, 290, 314, 626, 1784, 6041, 7556, 8876, 43181, 52454, 159731, 218084, 576239, 1478531, 2934539, 3085781, 3569114, 3802301, 4692866, 24307841, 25051934, 54168539, 285820856, 551855834, 742623164, 747988526, 1165052066, 3322447301

Offset: 1

Hugo Pfoertner, Mar 07 2024

nonn

			See A371002.

Hugo Pfoertner, Table of n, a(n) for n = 1..56 (terms a(1)-a(50) from Martin Ehrenstein)

A371002 gives the corresponding counts m.

Cf. A000290, A002808.

a371001_2(upto) = {my(n=0); forcomposite (k=4, upto, for (j=1, oo, if (isprime(k+j*j), if (j>n, print1([k,j-1],", "); n=j); break)))};
\\ change [k,j-1] in print1 to k or j-1 to mute the results for the other sequence
a371001_2(5000000)

A370999 Least composite number k such that the number m of consecutive composite sums k + j*(j+1)/2, j = 1, ..., m is a new maximum.

Original entry on oeis.org

4, 8, 9, 15, 24, 90, 105, 114, 225, 264, 300, 945, 5349, 7035, 11739, 17280, 35475, 46914, 190365, 351645, 603054, 1209900, 3146220, 3279864, 6407664, 26447649, 115192665, 408291345, 1080430119, 1298351109, 6459163344, 7731193299, 8096124894, 8884256514, 18927105834

Offset: 1

Karl-Heinz Hofmann and Hugo Pfoertner, Mar 09 2024

nonn

a(60) > 10^15.

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

A371000 gives the corresponding counts m.

Cf. A000217, A371001, A371002.

a(43) in b-file corrected by Kebbaj Mohamed Reda, May 29 2024

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).

Original entry on oeis.org

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

Karl-Heinz Hofmann and Hugo Pfoertner, Mar 09 2024

nonn

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.

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

Cf. A000217, A370999, A371001, A371002.

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)

cp's OEIS Frontend

A371001 Least number k such that the number m of consecutive composite sums k + j^2, j = 0, ..., m is a new maximum.

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A370999 Least composite number k such that the number m of consecutive composite sums k + j*(j+1)/2, j = 1, ..., m is a new maximum.

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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).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI