A246789 a(n) = A246778(A005669(n)).

2, 2, 4, 9, 18, 19, 34, 39, 42, 44, 74, 82, 87, 96, 129, 149, 150, 157, 184, 184, 194, 219, 259, 265, 293, 326, 343, 343, 370, 374, 418, 422, 441, 463, 468, 509, 539, 542, 548, 573, 627, 645, 659, 670, 671, 671, 687, 693, 708, 718, 750, 753, 771, 787, 845, 884, 904, 952, 999, 1040, 1055, 1169, 1193, 1193, 1428, 1446, 1475, 1547, 1552, 1579, 1590, 1601, 1604, 1657, 1704

Offset: 1

Author

Farideh Firoozbakht, Oct 08 2014

Keywords

• nonn
• hard

Comments

Conjecture: prime(A005669(n))^(1+1/A005669(n)) - prime(A005669(n)) is a strictly increasing function of n.

The truth of the conjecture would imply that "this sequence is an increasing sequence" which is another conjecture not equivalent to the first conjecture.

Note that if n is in the set {1, 19, 27, 45, 63} then a(n) = a(n+1) but there is no n, where n is less than 75 and a(n+1) < a(n).

Crossrefs

Cf. A000040, A002386, A005669, A246776, A246777, A246778.