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.

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

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

Author

Zak Seidov and Vladimir Shevelev, Dec 19 2011

Status

approved