A333541 -id:A333541 - cp's OEIS frontend

A333542 The primes missing from A333541.

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

A333537 Greatest prime factor of A332559.

Original entry on oeis.org

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 *)

A333538 Indices of records in A333537.

Original entry on oeis.org

1, 5, 21, 91, 355, 456, 666, 2927, 4946, 6064, 6188, 6192, 13858, 14884, 39592, 54429, 77603, 87566, 210905, 245770, 422097, 585876, 908602, 976209, 1240768, 1340675, 1573890, 2589172, 4740893, 5168099, 8525972, 8646462, 10478354, 12636785, 17943798, 19524935

Offset: 1

N. J. A. Sloane, Apr 12 2020

nonn

The first few primes that are not record values of A333537 are 2, 11, 53, 59, 71, 73, 89, 97, 103, 107 (see A333541, A333542). - Robert Israel, Apr 12 2020

a(72) > 5*10^9. - David A. Corneth, Apr 14 2020

David A. Corneth, Table of n, a(n) for n = 1..71 (first 36 terms from Robert Israel)
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. A061836, A332558, A332559, A333537, A333541, A333542.

f:= proc(n) local k, p;
  p:= n;
  for k from 1 do
    p:= p*(n+k);
    if (p/(n+k+1))::integer then return n+k+1 fi
  od
end proc:
R:= 1: g:= 3: count:= 1:
for n from 2 while count < 20 do
  x:= max(numtheory:-factorset(f(n)));
  if x > g then count:= count+1; g:= x; R:= R, n;  fi
od:
R; # Robert Israel, Apr 12 2020

f[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]]]]]];
R = {1}; g = 3; count = 1;
For[n = 2, count < 20, n++, x = f[n]; If[x > g, count++; g = x; AppendTo[R, n]]];
R (* Jean-François Alcover, Aug 17 2020, after Robert Israel *)

a(13)-a(20) from Robert Israel, Apr 12 2020

More terms from Jinyuan Wang, Apr 12 2020

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A333542 The primes missing from A333541.

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A333537 Greatest prime factor of A332559.

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A333538 Indices of records in A333537.

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