A130142 - OEIS

A130142

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

1, 3, 5, 7, 3, 11, 13, 53, 17, 19, 73, 23, 5, 9343, 29, 31, 113, -1, 37, 313, 41, 43

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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.

The value of a(17) is currently unknown.

LINKS

Table of n, a(n) for n=0..21.

EXAMPLE

n = 13: 2n+1 = 27 has nontrivial divisors 3 and 9, so we get 93, which has proper divisors 3 and 31, so we get 133.

Then 133 has nontrivial divisors 7 and 19, so we get 917.

Then 917 has nontrivial divisors 7 and 131, so we get 1317.

Then 1317 has nontrivial divisors 3 and 439, so we get 9343, a prime and a(13) = 9343.

From Sean A. Irvine, Sep 11 2009: (Start)

Proof chain for a(17). The following gives the argument to f at each step, followed by its factorization.

35 factors as 5 * 7.

75 has factors 3 * 5 * 5.

525153 has factors 3 * 193 * 907.

15057112727099753913 has factors 3 * 4463 * 17215189 * 65325353.

179719996575730910515106159846737337176838928854211713151146478934050745192125561494032705883138679506795913535235676554615981512719833136443 has factors 29 * 29 * 5546454298803948416569 * 8370112457804191610629 * 13338101723922940394396774098231 * 345111672681489292530961043464303237918570147336150469919363833

765...4892 (3249 digits) is divisible by 2, and hence all subsequent steps will be divisible by 2, therefore no prime is ever reached, therefore a(17)=-1. (End)

CROSSREFS

Cf. A130139, A130140, A130141, A120716.

Sequence in context: A100029 A099984 A130141 * A130139 A204938 A101088

Adjacent sequences: A130139 A130140 A130141 * A130143 A130144 A130145

KEYWORD

base,more,sign

AUTHOR

Adam L. Buchsbaum (alb(AT)research.att.com), Jul 30 2007, Aug 01 2007

EXTENSIONS

5 more terms (details for a(17) in example). Next term requires factoring a 1478-digit number. - Sean A. Irvine, Sep 11 2009

Edited by Michel Marcus, Mar 09 2023

STATUS

approved