cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

Views

Author

N. J. A. Sloane, Apr 12 2020

Keywords

Comments

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

Links

Crossrefs

Cf. A006530, A061836, A332558, A332559, A332560, A332561.
For records see A333538, A333541, A333542.

Programs

  • Mathematica
    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

Views

Author

N. J. A. Sloane, Apr 12 2020

Keywords

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

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

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

Views

Author

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

Keywords

Comments

For the primes that are not records, see A333542.

Examples

			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

Links

Crossrefs

Cf. A332558, A333537, A333538, A333542.

Extensions

More terms from David A. Corneth, Apr 21 2020
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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