A343021 Positions of records in A343016.

1, 2, 6, 90, 15120, 983010

Offset: 1

Author

J. M. Bergot and Robert Israel, Apr 02 2021

Keywords

• nonn
• more

Comments

Numbers k such that A343016(k) > A343016(j) for all j < k.

a(n) is divisible by 6 for n >= 3, by 30 for n >= 4, by 210 for n >= 5.

a(7) > 10^9 if it exists.

Examples

			A343016(1) = 0.
A343016(2) = 1 is the first value > 0 in A343016.
A343016(6) = 5 is the first value > 1.
A343016(90) = 6 is the first value > 5.
A343016(15120) = 7 is the first value > 6.
A343016(983010) = 8 is the first value > 7.
		

Crossrefs

Cf. A343016.

Programs

Maple

R:= 1,2:
vmax:= 2:
f:= proc(n) local s, t, k;
  s:= add(t[1]*t[2], t = ifactors(n)[2]);
  for k from 0 do if not isprime(k*n+s) then return k fi od;
end proc:
for n from 6 by 6 to 10^6 do
  v:= f(n);
  if v > vmax then
    vmax:= v;
    R:= R, n;
  fi
od:
R;

Mathematica

With[{s = Array[Block[{m = 0, k = Plus @@ Times @@@ FactorInteger[#]}, While[PrimeQ[# m + k], m++]; m] &, 10^6]}, Map[FirstPosition[s, #][[1]] &, Union@ FoldList[Max, s]]] (* Michael De Vlieger, Apr 13 2021 *)