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A059690 Number of distinct Cunningham chains of first kind whose initial prime (cf. A059453) falls into the interval [2^(n-1),2^n]. 1
1, 2, 2, 2, 3, 5, 7, 13, 20, 31, 52, 83, 142, 242, 412, 742, 1308, 2294, 4040, 7327, 13253, 24255, 44306, 81700, 150401, 277335, 513705, 954847, 1780466, 3325009, 6224182 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..31.

C. K. Caldwell, Cunningham Chains

W. Roonguthai, Yves Gallot's Proth.exe and Cunningham Chains

EXAMPLE

a(11)=21 means that between 1024 and 2048 exactly 21 primes introduce Cunningham chains: {1031, 1049, 1103, 1223, 1229, 1289, 1409, 1451, 1481, 1499, 1511, 1559, 1583, 1601, 1733, 1811, 1889, 1901, 1931, 1973, 2003}.

Their lengths are 2, 3 or 4. Thus the complete chains spread over more than one binary size-zone: e.g.{1409, 2819, 5639, 11279} The primes 1439 and 2879 also form a chain but 1439 is not at the beginning of that chain, 89 is.

MATHEMATICA

c = 0; k = 1; Do[ While[k <= 2^n, If[ PrimeQ[k] && !PrimeQ[(k - 1)/2] && PrimeQ[2k + 1], c++ ]; k++ ]; Print[c], {n, 1, 29}]

CROSSREFS

Cf. A023272, A023302, A023330, A005602, A007700, A053176, A059452-A059456, A059500, A057331, A059688, A007053, A036378, A029837, A007053.

Sequence in context: A291294 A014208 A243358 * A330310 A121256 A022867

Adjacent sequences:  A059687 A059688 A059689 * A059691 A059692 A059693

KEYWORD

nonn

AUTHOR

Labos Elemer, Feb 06 2001

EXTENSIONS

Edited and extended by Robert G. Wilson v, Nov 23 2002

STATUS

approved

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Last modified June 16 18:59 EDT 2021. Contains 345068 sequences. (Running on oeis4.)