[seqfan] permutation of nonnegative integers

[jnthn stdhr]

Begin with a=0 and b=1 and include any of [a, a+b, a*b, b], in that order,
not already in the sequence.  Increment a and b.  The sequence begins:

0, 1, 3, 2, 5, 6, 7, 12, 4, 9, 20, 11, 30, 13, 42, 15, 56, 8, 17, 72, 19,
90, 10, 21, 110, 23, 132, 25, 156, 27, 182, 14, 29, 210, 31,...

If a(n) is prime and a(n+1) is an even number, we get:

6, 12, 30, 42, 72, 90, 132, 210, 240, 342, 420, 462, 552, 702, 870, 930,
1122, 1260, 1332, 1560, 1722, 1980, 2352, 2550, 2652,...

which appears to be A024701 (a(n) = (-1 + prime(n+1)^2)/4.)

Of interest?