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A242462 a(1) = 10; for n>1, a(n) = (a(n-1)-1) * (smallest odd prime factor of a(n-1)) + 1. 0
10, 46, 1036, 7246, 26248636, 11628145306, 461742021916246, 7849614372576166, 44750651538056716666, 17139499539075722482696, 188534494929832947309646, 69192159639248691662639716, 2144956948816709441541831166, 13721289601580490297543093962506 (list; graph; refs; listen; history; text; internal format)
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 similarly defined 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^n-1 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
Conjecture is also true if it turns out that one number in this sequence is a multiple of either 19 or 73. Any number of the form 2^n-1 that is divisible by 19 is divisible by 27, and any number of the form 2^n-1 that is divisible by both 73 and 9 is divisible by 27. Numbers one less than this sequence are always divisible by 9 but not by 27. - J. Lowell, Feb 27 2022
LINKS
EXAMPLE
a(1) = 10; 10-1 = 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) opf(n) = n = n>>valuation(n, 2); if (n==1, 1, factor(n)[1, 1]);
lista(nn) = {a = 10; for (n=2, nn, olda = a; print1(a, ", "); a = 1 + (olda-1)*opf(olda); ); } \\ Michel Marcus, May 17 2014
CROSSREFS
Sequence in context: A351901 A219597 A000832 * A253477 A143895 A281767
KEYWORD
nonn
AUTHOR
J. Lowell, May 15 2014
EXTENSIONS
a(13)-a(14) and name change from Michel Marcus, May 17 2014
STATUS
approved

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Last modified February 22 22:43 EST 2024. Contains 370265 sequences. (Running on oeis4.)