A335293 a(n) is the positive integer with signature s that is the most frequent prime signature up to a(n)-1 such that there is a tie with a different signature. a(1) = 1.
1, 3, 58, 61, 65, 73, 77, 1279789, 1280057, 1280066, 1280073, 1280437, 1280441, 1281155, 1281161, 1281165, 1281179, 1281190, 1281243, 1281247, 1281262, 1281271, 1281313, 1281365
Offset: 1
Examples
Up to 57, primes and semiprimes occur equally often (16 times each). 58 is a semiprime, becoming the most frequently seen prime signature until then. Another tie occurs at 59 when primes are most frequently seen at 61 (18 times) but not at 60. Hence 61 is a term.