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A129733
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List of primitive prime divisors of the numbers (3^n-1)/2 (A003462) in their order of occurrence.
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6
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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; internal format)
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OFFSET
| 1,1
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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. [From T. D. Noe (noe(AT)sspectra.com), Mar 01 2010]
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REFERENCES
| G. Everest et al., Primes generated by recurrence sequences, Amer. Math. Monthly, 11 4 (No. 5, 2007), 417-431.
K. Zsigmondy, Zur Theorie der Potenreste, Monatsh. Math., 3 (1892), 265-284.
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LINKS
| T. D. Noe, Primes for n up to 500 (using the Cunningham tables)
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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;
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CROSSREFS
| Cf. A003462, A076481, A028491. If 3 is replaced by 2 we get A000225, A004668, A000043, A108974 respectively.
Sequence in context: A120863 A093079 A095417 * A084160 A176466 A128155
Adjacent sequences: A129730 A129731 A129732 * A129734 A129735 A129736
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), May 13 2007
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