The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 (list; graph; refs; listen; history; text; internal format)
 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 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^k-2^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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 24 12:42 EDT 2021. Contains 348231 sequences. (Running on oeis4.)