

A109291


New factors appearing in the factorization of 5^k  2^k as k increases.


0



3, 7, 13, 29, 1031, 19, 25999, 641, 5563, 11, 41, 1409, 11551, 541, 406898311, 1597, 31, 8161, 17, 22993, 82009, 3101039, 37, 397, 6357828601279, 61, 5521, 43, 1009, 3613, 23, 303293, 7591, 197479, 2650751, 380881, 151, 95801, 6660751, 53, 131, 25117, 1271899175923
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OFFSET

1,1


COMMENTS

Zsigmondy numbers for a = 5, b = 2: Zs(n, 5, 2) is the greatest divisor of 5^k  2^k that is relatively prime to 5^j  2^j for all positive integers j < k.


LINKS

Table of n, a(n) for n=1..43.
Eric Weisstein's World of Mathematics, Zsigmondy's Theorem


EXAMPLE

a(1) = 3 because 5^1  2^1 = 3.
a(2) = 7 because, although 5^2  2^2 = 21 = 3 * 7 has prime factor 3, that has already appeared in this sequence, but the factor of 7 is new.
a(3) = 13 because, although 5^3  2^3 = 117 = 3^2 * 13 has repeated prime factor 3, that has already appeared in this sequence, but the prime factor of 13 is new.
a(4) = 29 because, although 5^4  2^4 = 2385 = 609 = 3 * 7 * 29, the prime factors of 3 and 7 have already appeared in this sequence, but the prime factor of 29 is new.
a(5) = 1031 because, although 5^5  2^5 = 16775 = 3093 = 3 * 1031, the prime factor of 3 has already appeared in this sequence, but the prime factors of 1031 is new.


PROG

(PARI) lista(nn) = {my(pf = []); for (k=1, nn, f = factor(5^k2^k)[, 1]; for (j=1, #f~, if (!vecsearch(pf, f[j]), print1(f[j], ", "); pf = vecsort(concat(pf, f[j]))); ); ); } \\ Michel Marcus, Nov 13 2016


CROSSREFS

Cf. A109325, A109347, A109348, A109349, A109254.
Sequence in context: A091565 A025249 A147098 * A340067 A199218 A062700
Adjacent sequences: A109288 A109289 A109290 * A109292 A109293 A109294


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Aug 25 2005


EXTENSIONS

Comment corrected by Jerry Metzger, Nov 04 2009
More terms from Michel Marcus, Nov 13 2016


STATUS

approved



