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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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, May 13 2007
STATUS
approved

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Last modified May 29 12:15 EDT 2024. Contains 372940 sequences. (Running on oeis4.)