A129733 List of primitive prime divisors of the numbers (3^k-1)/2 (A003462) for k>=2, in order of their occurrence.

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

Offset

1,1

Comments

Read A003462 term-by-term, factorize each term, write down any primes not seen before.

Except for k=1, there is at least one primitive prime divisor for every k. - T. D. Noe, Mar 01 2010

Links

Max Alekseyev, Primes for k <= 690 (primes for k <= 500 from T. D. Noe)

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 with 2, we get A000225, 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