A333538 - OEIS

%I #29 Apr 25 2021 13:12:29

%S 1,5,21,91,355,456,666,2927,4946,6064,6188,6192,13858,14884,39592,

%T 54429,77603,87566,210905,245770,422097,585876,908602,976209,1240768,

%U 1340675,1573890,2589172,4740893,5168099,8525972,8646462,10478354,12636785,17943798,19524935

%N Indices of records in A333537.

%C 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

%C a(72) > 5*10^9. - _David A. Corneth_, Apr 14 2020

%H David A. Corneth, <a href="/A333538/b333538.txt">Table of n, a(n) for n = 1..71</a> (first 36 terms from Robert Israel)

%H J. S. Myers, R. Schroeppel, S. R. Shannon, N. J. A. Sloane, and P. Zimmermann, <a href="http://arxiv.org/abs/2004.14000">Three Cousins of Recaman's Sequence</a>, arXiv:2004:14000 [math.NT], April 2020.

%p f:= proc(n) local k, p;

%p   p:= n;

%p   for k from 1 do

%p     p:= p*(n+k);

%p     if (p/(n+k+1))::integer then return n+k+1 fi

%p   od

%p end proc:

%p R:= 1: g:= 3: count:= 1:

%p for n from 2 while count < 20 do

%p   x:= max(numtheory:-factorset(f(n)));

%p   if x > g then count:= count+1; g:= x; R:= R, n;  fi

%p od:

%p R; # _Robert Israel_, Apr 12 2020

%t 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]]]]]];

%t R = {1}; g = 3; count = 1;

%t For[n = 2, count < 20, n++, x = f[n]; If[x > g, count++; g = x; AppendTo[R, n]]];

%t R (* _Jean-François Alcover_, Aug 17 2020, after _Robert Israel_ *)

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

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Apr 12 2020

%E a(13)-a(20) from _Robert Israel_, Apr 12 2020

%E More terms from _Jinyuan Wang_, Apr 12 2020