A309387 a(n) is the smallest positive divisor not yet in the sequence of 7*A000217(n-1); n >= 1.

1, 7, 3, 2, 5, 15, 21, 4, 6, 9, 11, 14, 13, 49, 35, 8, 17, 51, 19, 10, 30, 33, 23, 12, 20, 25, 27, 18, 29, 87, 31, 16, 22, 77, 85, 42, 37, 133, 39, 26, 28, 41, 43, 86, 45, 63, 47, 24, 56, 175, 75, 34, 53, 159, 55, 44, 38, 57, 59, 70, 61, 217, 93, 32, 40, 65, 67, 119, 46, 69, 71, 36, 73, 259

Offset

1,2

Comments

Up to n=10000, 1166 of the first 1228 odd primes appear as fixed points of a(n), i.e., 95%.

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..74.

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 7*0 not yet in the sequence.
For n = 23: a(23) = 23 is a fixed point and the smallest divisor of 7*253 not yet in the sequence.
For n = 73: a(73) = 73 is a fixed point and the smallest divisor of 7*2628 not yet in the sequence.

Crossrefs

Cf. A000217, A111273, A309275, A309276.

Sequence in context: A098907 A153205 A340485 * A298530 A243377 A245532

Adjacent sequences: A309384 A309385 A309386 * A309388 A309389 A309390

Keyword

nonn

Author

Enrique Navarrete, Jul 27 2019

Status

approved