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A181715 Length of the complete Cunningham chain of the second kind starting with prime(n). 8
3, 2, 1, 2, 1, 1, 1, 3, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Number of iterations x -> 2x-1 needed to get a composite number, when starting with prime(n).
Dickson's conjecture implies that, for every positive integer r, there exist infinitely many n such that a(n) = r. - Lorenzo Sauras Altuzarra, Feb 12 2021
a(n) is the least k such that 2^k * (prime(n)-1) + 1 is composite. Note that a(n) is well defined since 2^(p-1) * (p-1) + 1 is divisible by p for odd primes p. - Jianing Song, Nov 24 2021
LINKS
G. Löh, Long chains of nearly doubled primes, Math. Comp., 53 (1989), 751-759.
Michael Penn, Romanian Mathematical Olympiad Problem, Youtube video, 2020.
Wikipedia, Cunningham chain
FORMULA
a(n) < prime(n) for n > 1; see Löh (1989), p. 751. - Jonathan Sondow, Oct 28 2015
max(a(n), A181697(n)) = A263879(n) for n > 2. - Jonathan Sondow, Oct 30 2015
a(n) = A285700(A000040(n)). - Antti Karttunen, Apr 26 2017
EXAMPLE
2 -> 3 -> 5 -> 9 = 3^2, so a(1) = 3 and a(2) = 2. - Jonathan Sondow, Oct 30 2015
MAPLE
a := proc(n)
local c, l:
c, l := 0, ithprime(n):
while isprime(l) do c, l := c+1, 2*l-1: od:
c:
end: # Lorenzo Sauras Altuzarra, Feb 12 2021
MATHEMATICA
Table[p = Prime[n]; cnt = 1; While[p = 2*p - 1; PrimeQ[p], cnt++]; cnt, {n, 100}] (* T. D. Noe, Jul 12 2012 *)
Table[-1 + Length@ NestWhileList[2 # - 1 &, Prime@ n, PrimeQ@ # &], {n, 98}] (* Michael De Vlieger, Apr 26 2017 *)
PROG
(PARI) a(n)= n=prime(n); for(c=1, 1e9, is/*pseudo*/prime(n=2*n-1) || return(c))
CROSSREFS
Cf. A137288 (positions of terms > 1).
Sequence in context: A331539 A306287 A016457 * A077089 A156352 A175191
KEYWORD
nonn
AUTHOR
M. F. Hasler, Nov 17 2010
EXTENSIONS
Escape clause added to definition by N. J. A. Sloane, Feb 19 2021
Escape clause deleted from definition by Jianing Song, Nov 24 2021
STATUS
approved

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Last modified June 16 14:12 EDT 2024. Contains 373430 sequences. (Running on oeis4.)