A333538 Indices of records in A333537.

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

Author

N. J. A. Sloane, Apr 12 2020

Keywords

• nonn

Comments

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

Links

• 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.

Crossrefs

Cf. A061836, A332558, A332559, A333537, A333541, A333542.

Programs

Maple

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

Mathematica

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 *)

Extensions

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

More terms from Jinyuan Wang, Apr 12 2020