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A202397 Length of period of sequence starting with a(1)=prime(n), a(2)=prime(n+1) and a(n>2)=2(gpd(a(n-1))+gpd(a(n-2)))+1, where gpd(m) is the greatest prime divisor of m. 1
24, 3, 3, 51, 3, 24, 24, 51, 24, 24, 24, 24, 24, 3, 3, 51, 24, 24, 24, 24, 3, 51, 24, 24, 24, 51, 24, 42, 3, 24, 51, 51, 24, 24, 24, 24, 51, 24, 24, 24, 51, 51, 24, 24, 51, 24, 3, 24, 24, 24, 24, 24, 10, 24, 51, 24, 24, 24, 24, 24, 42, 51, 3, 51, 51, 51, 24 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The case n=1 was considered in A202211.

Astonishingly, for n = 1..10000 there are only 5 different periods with lengths 3, 10, 24, 42, 51.

Corresponding frequencies of periods for n = 1..10000 are {726, 543, 6116, 170, 2445}.

Suggestion: there is no initial pair {a(1),a(2)} giving a non-periodic sequence. There may also be other periods.

LINKS

Zak Seidov, Table of n, a(n) for n = 1..10000

EXAMPLE

List of periods:

{21, 25, 25}, (other 3-period: {33,33,45})

{61, 137, 397, 1069, 2933, 2977, 1297, 3053, 2737, 189},

{53, 113, 333, 301, 161, 133, 85, 73, 181, 509, 1381, 3781, 3161, 617, 1453, 4141, 3109, 6421, 19061, 13621, 1293, 1377, 897, 81},

{157, 353, 1021, 2749, 7541, 20581, 18825, 4245, 1069, 2705, 3221, 7525, 6529, 13145, 13537, 27553, 28009, 2449, 1673, 637, 505, 229, 661, 1781, 1597, 3469, 10133, 27205, 31149, 17805, 9297, 4441, 10949, 30781, 83461, 85409, 24613, 1093, 2513, 2905, 885, 285},

{93, 97, 257, 709, 1933, 5285, 4169, 1061, 2881, 2257, 257, 637, 541, 1109, 3301, 8821, 24245,18389, 889, 397, 1049, 2893, 2625, 541, 1097, 3277, 2421, 765, 573, 417, 661, 1601, 4525, 3565, 425, 97, 229, 653, 1765, 2013, 829, 1781, 1933, 4141, 4069, 829, 2285, 2573, 1081, 261,153}.

CROSSREFS

Cf. A202211.

Sequence in context: A159540 A040564 A040565 * A040566 A070707 A126653

Adjacent sequences:  A202394 A202395 A202396 * A202398 A202399 A202400

KEYWORD

nonn,changed

AUTHOR

Zak Seidov and Vladimir Shevelev, Dec 19 2011

STATUS

approved

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Last modified September 23 13:56 EDT 2021. Contains 347617 sequences. (Running on oeis4.)