A333538 -id:A333538 - cp's OEIS frontend

A333537 Greatest prime factor of A332559.

3, 3, 3, 2, 5, 3, 3, 3, 5, 5, 3, 3, 5, 5, 5, 3, 3, 3, 3, 3, 7, 5, 5, 5, 5, 7, 7, 7, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 3, 3, 3, 3, 5, 5, 13, 7, 7, 7, 7, 7, 7, 7, 3, 7, 7, 7, 7, 7, 7, 5

Offset: 1

N. J. A. Sloane, Apr 12 2020

nonn

For rate of growth, see the Myers et al. link. - N. J. A. Sloane, Apr 30 2020

N. J. A. Sloane, Table of n, a(n) for n = 1..10000.
J. S. Myers, R. Schroeppel, S. R. Shannon, N. J. A. Sloane, and P. Zimmermann, Three Cousins of Recaman's Sequence, arXiv:2004:14000 [math.NT], April 2020.

Cf. A006530, A061836, A332558, A332559, A332560, A332561.

For records see A333538, A333541, A333542.

a[n_] := Module[{k, p = n}, For[k = 1, True, k++, p *= (n+k); If[Divisible[ p, n+k+1], Return[FactorInteger[n+k+1][[-1, 1]]]]]];
Array[a, 1000] (* Jean-François Alcover, Aug 17 2020 *)

A333541 Records in A333537.

Original entry on oeis.org

3, 5, 7, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 61, 67, 79, 83, 101, 109, 113, 137, 139, 149, 151, 157, 167, 199, 211, 227, 239, 257, 269, 277, 283, 307, 313, 317, 353, 373, 379, 389, 397, 409, 433, 439, 499, 503, 569, 571, 593, 607, 617, 631, 701, 709, 727, 743, 757, 769, 773

Offset: 1

N. J. A. Sloane, Apr 20 2020, using data from Robert Israel's comment in A333538

nonn

For the primes that are not records, see A333542.

			For n = 91 as A332558(91) = 12 we have (91 + A332558(91) + 1) = (91 + 12 + 1) | (91 * 92 * ... * (91 + 12)) = (91 * 92 * ... * (91 + A332558(91))). The largest prime factor of 91 + 12 + 1 = 104 is 13. For no m < 91 the largest prime factor of m + A332558(m) + 1 = A332559(m) is at least 13 so 13 is a new record in A333537. - _David A. Corneth_, Apr 21 2020

David A. Corneth, Table of n, a(n) for n = 1..71
J. S. Myers, R. Schroeppel, S. R. Shannon, N. J. A. Sloane, and P. Zimmermann, Three Cousins of Recaman's Sequence, arXiv:2004:14000 [math.NT], April 2020.

Cf. A332558, A333537, A333538, A333542.

More terms from David A. Corneth, Apr 21 2020

A333542 The primes missing from A333541.

Original entry on oeis.org

2, 11, 53, 59, 71, 73, 89, 97, 103, 107, 127, 131, 163, 173, 179, 181, 191, 193, 197, 223, 229, 233, 241, 251, 263, 271, 281, 293, 311, 331, 337, 347, 349, 359, 367, 383, 401, 419, 421, 431, 443, 449, 457, 461, 463, 467, 479, 487, 491, 509, 521, 523, 541, 547, 557, 563

Offset: 1

N. J. A. Sloane, Apr 20 2020

nonn

These are the primes that are not record high values in A333537.

			We have A333541(k) = 7 for some k and the term after that A333541(k + 1) = 13. As 11 is a prime between 7 and 13, 11 is in the sequence. - _David A. Corneth_, Apr 21 2020

David A. Corneth, Table of n, a(n) for n = 1..100
J. S. Myers, R. Schroeppel, S. R. Shannon, N. J. A. Sloane, and P. Zimmermann, Three Cousins of Recaman's Sequence, arXiv:2004:14000 [math.NT], April 2020.

Cf. A332558, A333537, A333538, A333541.

More terms from David A. Corneth, Apr 21 2020

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A333537 Greatest prime factor of A332559.

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A333541 Records in A333537.

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A333542 The primes missing from A333541.

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