A377120 - OEIS

A377120

a(n) = number of iterations of x -> 2 x + 3 to reach a nonprime, starting with prime(n) .

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

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OFFSET

1,1

COMMENTS

Guide to related sequences:

mapping initial prime sequence

x -> 2x + 1 2 A181697

x -> 2x + 3 2 this sequence

x -> 2x + 5 2 A377510

x -> 2x + 7 2 A377511

x -> 2x - 1 2 A181715

x -> 2x - 3 5 A377512

x -> 2x - 5 7 A377513

x -> 2x - 7 11 A377514

LINKS

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

EXAMPLE

prime(1) = 2 -> 7 -> 17 -> 37 -> 77 = 7*11, so a(1) = 4.

MAPLE

f:= proc(p) local x, i;

x:= p;

for i from 1 do

x:= 2*x+3;

if not isprime(x) then return i fi;

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 + 3; PrimeQ[p], c++]; c, {n, 200}]

CROSSREFS

Cf. A000040, A181697, A181715, A377510, A377511, A377512, A377513, A377514.

Sequence in context: A324937 A388747 A049007 * A016686 A060037 A229705

Adjacent sequences: A377117 A377118 A377119 * A377121 A377122 A377123

KEYWORD

nonn

AUTHOR

Clark Kimberling, Oct 31 2024

STATUS

approved