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A227202
Least prime, q, greater than the previous prime, p, which is a primitive root of p; beginning with 2.
0
2, 3, 5, 7, 11, 13, 19, 23, 47, 59, 61, 67, 71, 83, 89, 101, 103, 107, 113, 137, 149, 163, 167, 179, 181, 191, 211, 227, 233, 257, 263, 277, 283, 311, 331, 347, 349, 359, 373, 397, 419, 421, 431, 443, 449, 461, 463, 467, 479, 499, 503, 577, 587, 593, 599, 613, 619, 647, 677, 709
OFFSET
1,1
COMMENTS
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, …; .
a(10^k), k-0… = 2, 59, 1439, 22543, 298943, 3671543, 43346683, 498427109, …, .
Conjecture: a(n) < Prime[n*E].
The first prime absent from the sequence is 17, but it will join this sequence at 23.
The second prime absent from this sequence is 29, but it will join this sequence by going through 41 and then 47.
The third prime absent is 31 which joins at 47.
Conjecture: All primes will join this sequence eventually.
EXAMPLE
a(7) is not 17 because (13,17) = 1 but is 19 because (13,19) = -1.
MATHEMATICA
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]
CROSSREFS
Cf. A060085.
Sequence in context: A030145 A285983 A020588 * A237827 A114111 A155108
KEYWORD
nonn,easy
AUTHOR
Robert G. Wilson v, Sep 18 2013
STATUS
approved