A343016 -id:A343016 - cp's OEIS frontend

A343021 Positions of records in A343016.

1, 2, 6, 90, 15120, 983010

Offset: 1

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

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.

			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.

Cf. A343016.

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;

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 *)

A342302 Numbers k such that A001414(k), k+A001414(k) and 2*k+A001414(k) are prime.

Original entry on oeis.org

6, 12, 48, 90, 252, 294, 300, 420, 432, 720, 798, 864, 930, 1020, 1140, 1218, 1368, 1428, 1602, 1716, 1890, 1938, 2088, 2184, 2190, 2196, 2250, 2760, 2880, 3588, 3660, 3708, 3774, 3810, 4452, 4710, 4902, 5280, 5340, 5412, 5754, 5850, 6174, 6240, 6462, 6768, 7014, 7182, 7632, 8322, 8820, 9144

Offset: 1

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

nonn

Numbers k such that A343016(k) >= 3.

All terms are divisible by 6.

			a(3) = 48 = 2^4*3 is a term because A001414(48) = 4*2+3 = 11 and 11, 48+11 = 59 and 2*48+11 = 107 are prime.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A001414, A343016.

filter:= proc(n) local s,t;
s:= add(t[1]*t[2], t=ifactors(n)[2]);
isprime(s) and isprime(n+s) and isprime(2*n+s)
end proc;
select(filter, [seq(i,i=6..10000,6)]);

cp's OEIS Frontend

A343021 Positions of records in A343016.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Maple

Mathematica