

A242462


a(1) = 10; for n>1, a(n) = (a(n1)1) * (smallest odd prime factor of a(n1)) + 1.


0



10, 46, 1036, 7246, 26248636, 11628145306, 461742021916246, 7849614372576166, 44750651538056716666, 17139499539075722482696, 188534494929832947309646, 69192159639248691662639716, 2144956948816709441541831166, 13721289601580490297543093962506
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OFFSET

1,1


COMMENTS

Note: this sequence will terminate if a power of 2 occurs.
Conjecture: this sequence is infinite (so it contains no powers of 2). The similar sequence starting with a(1) = 6 terminates after 2 terms: 6 and 16.
Conjecture is true if it turns out that one number in this sequence is one more than a multiple of 41. Any number of the form 2^n1 that is divisible by 41 is also divisible by 25, which is the square of a prime number greater than 3. Because numbers one less than this sequence's terms are always 9 times a squarefree number, this proves that if a number one less than this sequence is divisible by 41, then this sequence is infinite.  J. Lowell, Jul 17 2017


LINKS

Table of n, a(n) for n=1..14.


EXAMPLE

a(1) = 10; 101 = 9; 9*5 (smallest odd prime factor of 10) is 45; 45+1=46, so a(2) = 46.


MATHEMATICA

NestList[DeleteCases[FactorInteger[#], w_ /; First@ w == 2][[1, 1]] (#  1) + 1 &, 10, 13] (* Michael De Vlieger, Jul 18 2017 *)


PROG

(PARI) lista(nn) = {a = 10; for (n=2, nn, olda = a; print1(a, ", "); a = 1 + (olda1)*opf(olda); ); } \\ Michel Marcus, May 17 2014


CROSSREFS

Sequence in context: A138041 A219597 A000832 * A253477 A143895 A281767
Adjacent sequences: A242459 A242460 A242461 * A242463 A242464 A242465


KEYWORD

nonn


AUTHOR

J. Lowell, May 15 2014


EXTENSIONS

a(13)a(14) and name change from Michel Marcus, May 17 2014


STATUS

approved



