A377510 a(n) = number of iterations of x -> 2 x + 5 to reach a nonprime, starting with prime(n).

1, 2, 1, 3, 1, 6, 1, 2, 1, 1, 5, 4, 1, 1, 1, 1, 1, 2, 4, 1, 4, 3, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 3, 1, 3, 1, 2, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 4, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1

Offset

1,2

Comments

See A377120 for a guide to related sequences.

Links

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

Example

prime(6) = 13 -> 31 -> 67 -> 139 -> 283 -> 571 -> 1147 = 31*37, so a(6) = 6.

Maple

f:= proc(p) local x, i;
  x:= p;
  for i from 1 do
    x:= 2*x+5;
    if not isprime(x) then return i fi;
  od
end proc:
map(f, [seq(ithprime(i), i=1..100)]); # Robert Israel, Nov 17 2025

Mathematica

Table[p = Prime[n]; c = 1; While[p = 2*p + 5; PrimeQ[p], c++]; c, {n, 200}]

Crossrefs

Cf. A377120, A377511, A377512, A377513, A377514.

Sequence in context: A347982 A321738 A022458 * A084419 A119606 A034850

Adjacent sequences: A377507 A377508 A377509 * A377511 A377512 A377513

Keyword

nonn

Author

Clark Kimberling, Oct 31 2024

Status

approved