Michael De Vlieger, <a href="/A362631/b362631_1.txt">Table of n, a(n) for n = 1..10000</a>

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Some primes (23,29,31,47,...) enter because of dividing a(n-2) but not a(n-1), whereas others (5,7,11,13,17,19,...) enter as least u; see Example.

a(4,5) = 4, 6 and since rad(4)|rad(6) a(6) = least u = 5.

a(11,12) = 8, 20 and since rad(8)|rad(20) a(13) = least u = 7.

a(44,45) = 132, 13 and gpd(132) = 11 does not divide 13, and since it is the 13th occurrence of p = 11, a(46) = 13*11 = 143.

a(45,46) = 13, 143 which forces a(47) = least u = 16 (see Comment).

a(90,91) = 69, 114 and 23 is the greatest prime dividing 69 which does not divide 114. Since 23 has not appeared earlier in the sequence a(92) = 23.

There is as yet no known formula for the row lengths of the table below. Whereas most rows terminate with a multiple of the prime they start with, there are exceptions, e.g. , 47, 109. This behavior is open to explanation.

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The sequence, after a(1) = 1 can be represented as an irregular table in which the nth n-th row starts with prime(n), see Example.

There is as yet no known formula for the row lengths of the table below. Whereas most rows terminate with a multiple of the prime they start with, there are exceptions, e.g. 47,109. This behaviour behavior is open to explanation.

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Lexicographically earliest infinite sequence of distinct positive integers with a(n) = n for n <= 3, and for n > 3 a(n) is the least novel multiple of the greatest prime divisor of a(n-2) which does not divide a(n-1).

Lexicographically earliest sequence of distinct positive integers commencing with a(n) = n for n <= 3, and thereafter: for n > 3 a(n) is either (i). the least novel multiple m of the greatest prime divisor p of a(n-2) which does not divide a(n-1), or (ii). the least unused number (u), if no such prime exists.

The definition reflects that of A098550 in that it places a condition on a(n-2) which does not apply to a(n-1). However here adjacent terms, though often coprime to each other, are are not forced to be so.

a(n) = u iff rad(a(n-2)|rad(a(n-1). For example when If there is no prime divisor of a(n-2) = 2^k and which does not divide a(n-1) is even , then by empty product convention a(n) = u; see Example the least unused number.

Some primes (23,29,31,47...) enter the sequence consequent to the first part because of the definition, dividing a(n-2) but not a(n-1), whereas others (5,7,11,13,17,19...) enter as "least u"; see Example.

With the exception of a(47) = 16 all least u terms (up to a(2^28)) are primes, and so it seems likely that a(47) = 16 is a one-off (fluke) term.

a(90,91) = 69,114 and 23 is the greatest prime dividing 69 which does not divide 114. Since 23 has not appeared earlier in the sequence a(92) = 23.

There is as yet no known formula for the row lengths of the table below. Whereas most rows terminate with a multiple of the primes prime they start with, there are exceptions, e.g. 47,109 (both resulting from the first part of the definition). This behaviour is open to explanation. The table starts:

The table starts:

Cf. A007947, A098550, A361629, A361133, A361534, A362855.