A227202 Least prime, q, greater than the previous prime, p, which is a primitive root of p; beginning with 2.

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.

Links

Table of n, a(n) for n=1..60.

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

Adjacent sequences: A227199 A227200 A227201 * A227203 A227204 A227205

Keyword

nonn,easy

Author

Robert G. Wilson v, Sep 18 2013

Status

approved