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 A129733 List of primitive prime divisors of the numbers (3^n-1)/2 (A003462) in their order of occurrence. 6
 2, 13, 5, 11, 7, 1093, 41, 757, 61, 23, 3851, 73, 797161, 547, 4561, 17, 193, 1871, 34511, 19, 37, 1597, 363889, 1181, 368089, 67, 661, 47, 1001523179, 6481, 8951, 391151, 398581, 109, 433, 8209, 29, 16493, 59, 28537, 20381027, 31, 271, 683 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Read A003462 term-by-term, factorize each term, write down any primes not seen before. Except for n=2, there is at least one primitive prime divisor for every n. - T. D. Noe, Mar 01 2010 LINKS T. D. Noe, Primes for n up to 500 (using the Cunningham tables) G. Everest et al., Primes generated by recurrence sequences, Amer. Math. Monthly, 114 (No. 5, 2007), 417-431. K. Zsigmondy, Zur Theorie der Potenzreste, Monatsh. Math., 3 (1892), 265-284. MAPLE # produce sequence s1:=(a, b, M)->[seq( (a^n-b^n)/(a-b), n=0..M)]; # find primes and their indices s2:=proc(s) local t1, t2, i; t1:=[]; t2:=[]; for i from 1 to nops(s) do if isprime(s[i]) then t1:=[op(t1), s[i]]; t2:=[op(t2), i-1]; fi; od; RETURN(t1, t2); end; # get primitive prime divisors in order s3:=proc(s) local t2, t3, i, j, k, np; t2:=[]; np:=0; for i from 1 to nops(s) do t3:=ifactors(s[i])[2]; for j from 1 to nops(t3) do p := t3[j][1]; new:=1; for k from 1 to np do if p = t2[k] then new:= -1; break; fi; od; if new = 1 then np:=np+1; t2:=[op(t2), p]; fi; od; od; RETURN(t2); end; CROSSREFS Cf. A003462, A076481, A028491. If 3 is replaced by 2 we get A000225, A004668, A000043, A108974 respectively. Sequence in context: A095417 A369587 A366719 * A084160 A238139 A268722 Adjacent sequences: A129730 A129731 A129732 * A129734 A129735 A129736 KEYWORD nonn AUTHOR N. J. A. Sloane, May 13 2007 STATUS approved

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