|
%I #7 Sep 22 2013 03:20:50
%S 2,3,5,7,11,13,19,23,47,59,61,67,71,83,89,101,103,107,113,137,149,163,
%T 167,179,181,191,211,227,233,257,263,277,283,311,331,347,349,359,373,
%U 397,419,421,431,443,449,461,463,467,479,499,503,577,587,593,599,613,619,647,677,709
%N Least prime, q, greater than the previous prime, p, which is a primitive root of p; beginning with 2.
%C a(12^k), k-0… = 2, 3, 7, 23, 101, 277, 823, 1871, 4649, 10369, 23087, 51407, 111779, 240059, 515597, 1100831, 2321563, 4916957, 10370993, 21771443, 45592199, 95294021, 198746747, 413993303, 860461453, …; .
%C a(10^k), k-0… = 2, 59, 1439, 22543, 298943, 3671543, 43346683, 498427109, …, .
%C Conjecture: a(n) < Prime[n*E].
%C The first prime absent from the sequence is 17, but it will join this sequence at 23.
%C The second prime absent from this sequence is 29, but it will join this sequence by going through 41 and then 47.
%C The third prime absent is 31 which joins at 47.
%C Conjecture: All primes will join this sequence eventually.
%e a(7) is not 17 because (13,17) = 1 but is 19 because (13,19) = -1.
%t f[s_] := Block[{p = s[[-1]], q = NextPrime[s[[-1]]]}, While[ MultiplicativeOrder[p, q] + 1 != q, q = NextPrime[q]]; Append[s, q]]; Nest[f, {2}, 60]
%Y Cf. A060085.
%K nonn,easy
%O 1,1
%A _Robert G. Wilson v_, Sep 18 2013
|
