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A377512
a(n) = number of iterations of x -> 2 x - 3 to reach a nonprime, starting with prime(n+2).
6
4, 3, 2, 5, 3, 1, 4, 1, 2, 3, 2, 3, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 3, 2, 1, 3, 1, 4, 3, 1, 2, 1, 1, 1, 3, 1, 3, 1, 1, 2, 2, 2, 1, 1, 2, 3, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 1, 1, 7, 1, 1, 2, 1, 3, 2, 1, 2, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 1, 2, 1, 2
OFFSET
1,1
COMMENTS
See A377120 for a guide to related sequences.
LINKS
EXAMPLE
prime(3) = 5 -> 7 -> 11 -> 19 -> 35 = 5*7, 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;
od
end proc:
map(f, [seq(ithprime(i+2), i=1..100)]); # Robert Israel, Nov 17 2025
MATHEMATICA
Table[p = Prime[n+2]; c = 1; While[p = 2*p - 3; PrimeQ[p], c++]; c, {n, 200}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Nov 05 2024
EXTENSIONS
Definition corrected by Robert Israel, Nov 17 2025
STATUS
approved