A309276 a(n) is the smallest divisor not yet in the sequence of 5*T(n)= 5*n(n-1)/2, where T(n) are the triangular numbers; n => 1.

1, 5, 3, 2, 10, 15, 7, 4, 6, 9, 11, 22, 13, 35, 21, 8, 17, 45, 19, 25, 14, 33, 23, 12, 20, 65, 27, 18, 29, 75, 31, 16, 24, 51, 85, 30, 37, 95, 39, 26, 41, 105, 43, 55, 50, 69, 47, 40, 28, 49, 125, 34, 53, 135, 99, 44, 38, 57, 59, 118, 61, 155, 63, 32, 52, 143, 67, 134, 46, 115, 71

Offset

1,2

Comments

Up to n = 10000, 1145 of the first 1228 odd primes appear as fixed points of a(n).

Links

Table of n, a(n) for n=1..71.

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

Example

For n = 1, 5*T(1) = 0, and a(1) = 1 is the smallest divisor of 0 not yet in the sequence.
For n = 3, 5*T(3) = 15, and a(3) = 3 is a fixed point and the smallest divisor of 15 not yet in the sequence.
For n = 71, 5*T(71) = 2485, and a(71) = 71 is a fixed point and the smallest divisor of 2485 not yet in the sequence.

Crossrefs

Cf. A000217, A111273.

Sequence in context: A222362 A352024 A176524 * A268690 A065627 A193958

Adjacent sequences: A309273 A309274 A309275 * A309277 A309278 A309279

Keyword

nonn

Author

Enrique Navarrete, Jul 20 2019

Status

approved