cp's OEIS Frontend

Differs from A000027(n) = n (positive integers) from a(193) = 191 on.

For all i, j: a(i) = a(j) => A317838(i) = A317838(j).

There are certain prime pairs p, q for which the Stern polynomials B(p,t) and B(q,t) (see table A125184) have equal multisets of nonzero coefficients. For example, for primes 191 and 193 these coefficients are {1, 2, 2, 2, 2, 3, 1} and {1, 2, 2, 2, 3, 2, 1} (from which follows that A278243(191) = A278243(193), A286378(191) = A286378(193) and thus => a(191) = a(193) => A002487(191) = A002487(193) as well). Other such prime pairs currently known are {419, 461}, {2083, 2143} and {11777, 12799}. Whenever a(p) = a(q) for such a prime pair, then also a(2^k * p) = a(2^k * q) for all k >= 0. It would be nice to know whether there could exist any other cases of a(i) = a(j), i != j, but for example both i and j being odd semiprimes?

This sequence works as a "sentinel" for A273671 by matching to any sequence that is obtained as f(A273671(n)), where f(n) is any function that depends only on the prime signature of n (see the index entry for "sequences computed from exponents in ..."). The only other sequence that as of Nov 11 2016 seems to match is A106347, although more terms of the latter would be needed to better ascertain whether the connection is spurious or genuine.