A309275 a(n) is the smallest divisor not yet in the sequence of 3*T(n)= 3*n(n-1)/2, where T(n) are the triangular numbers; n => 1.

1, 3, 9, 2, 5, 15, 7, 4, 6, 27, 11, 18, 13, 21, 35, 8, 12, 17, 19, 10, 14, 33, 23, 36, 20, 25, 39, 42, 29, 45, 31, 16, 22, 51, 85, 30, 37, 57, 117, 26, 41, 63, 43, 66, 54, 69, 47, 24, 28, 49, 75, 34, 53, 81, 55, 44, 38, 87, 59, 90, 61, 93, 189, 32, 40, 65, 67, 102

Offset

1,2

Comments

Up to n = 10000, 1160 of the first 1228 odd primes appear as fixed points of a(n).

Links

Table of n, a(n) for n=1..68.

Enrique Navarrete and Daniel Orellana, Finding Prime Numbers as Fixed Points of Sequences, arXiv:1907.10023 [math.NT], 2019.

Example

For n = 7, 3*T(7) = 63, and a(7) = 7 is a fixed point and the smallest divisor of 63 not yet in the sequence.
For n = 43, 3*T(43) = 2709, and a(43) = 43 is a fixed point and the smallest divisor of 2709 not yet in the sequence.

Crossrefs

Cf. A000217, A111273.

Sequence in context: A103824 A155080 A010780 * A179655 A357472 A076420

Adjacent sequences: A309272 A309273 A309274 * A309276 A309277 A309278

Keyword

nonn

Author

Enrique Navarrete, Jul 20 2019

Status

approved