A309389 a(n) is the smallest positive divisor not yet in the sequence of 11*A000217(n-1); n >= 1.

1, 11, 3, 2, 5, 15, 7, 4, 6, 9, 55, 22, 13, 77, 21, 8, 17, 33, 19, 10, 14, 121, 23, 12, 20, 25, 27, 18, 29, 87, 31, 16, 24, 51, 35, 30, 37, 209, 39, 26, 41, 123, 43, 86, 45, 69, 47, 44, 28, 49, 75, 34, 53, 99, 135, 70, 38, 57, 59, 66, 61, 341, 63, 32, 40, 65, 67, 134, 46, 105, 71, 36, 73, 407, 111

Offset

1,2

Comments

Up to n=10000, 1176 of the first 1228 odd primes appear as fixed points of a(n), i.e., 95.8%.

Conjecture: for large p prime, the odd primes (except p) appear as fixed points of b(n), where b(n) is the smallest positive divisor not yet in the sequence of p*A000217(n-1); n >= 1 (see link).

Links

Table of n, a(n) for n=1..75.

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

Example

For n = 1: a(1) = 1 is the smallest divisor of 11*0 not yet in the sequence.
For n = 23: a(23) = 23 is a fixed point and the smallest divisor of 11*253 not yet in the sequence.
For n = 73: a(73) = 73 is a fixed point and the smallest divisor of 11*2628 not yet in the sequence.

Crossrefs

Cf. A000217, A111273, A309275, A309276, A309387.

Sequence in context: A355369 A140749 A010188 * A110089 A177415 A208091

Adjacent sequences: A309386 A309387 A309388 * A309390 A309391 A309392

Keyword

nonn

Author

Enrique Navarrete, Jul 27 2019

Status

approved