A130140 Let f denote the map that replaces k with the concatenation of its nontrivial divisors, written in increasing order, each divisor being written in base 10 with its digits in reverse order. Then a(n) = prime reached when starting at 2n+1 and iterating f.

1, 3, 5, 7, 3, 11, 13

Offset

0,2

Comments

If 2n+1 is 1 or a prime, set a(n) = 2n+1. If no prime is ever reached, set a(n) = -1.

Links

Table of n, a(n) for n=0..6.

Example

n = 7: 2n+1 = 15 = 3*5 -> 35 = 5*7 -> 57 = 3*19 -> 391 = 17*23 -> 7132.
Then 7132 has nontrivial divisors 2, 4, 1783, 3566, so we get 2438716653.
Then 2438716653 has nontrivial divisors 3, 9, 27, 81, 243, 1453, 4359, 6907, 13077, 20721, 39231, 62163, 117693, 186489, 353079, 559467, 1678401, 10035871, 30107613, 90322839, 270968517, 812905551, so we get
397218342354195347096770311270213293361263967119846819703537649551048761178530013167010393822309715869072155509218 = 2*3^4*1217*317539*1211548321*33378971294653*8960783431807*17509226460292689821646170308388500174366980857582533580184934929433.

Crossrefs

Cf. A130139, A130141, A130142, A120716.

Sequence in context: A156030 A338974 A255562 * A051417 A326577 A090368

Adjacent sequences: A130137 A130138 A130139 * A130141 A130142 A130143

Keyword

base,more,nonn

Author

David Applegate, Jul 30 2007

Extensions

Edited by Michel Marcus, Mar 09 2023

Status

approved