A373626 Least prime of a run of n consecutive primes p_i, i = 1..n, such that bigomega(p_i + 1) = omega(p_i + 1) + i and bigomega(p_(n+1) + 1) <> omega(p_(n+1) + 1) + n + 1, or -1 if no such prime exists.

3, 19, 739, 76913, 4510333, 746264059, 290623032907

Offset

1,1

Links

Table of n, a(n) for n=1..7.

Example

19 starts a run of 2 consecutive primes 19 and 23, bigomega(19+1) = 2 = omega(19+1) + 1, bigomega(23+1) = 4 = omega(23+1) + 2 and bigomega(29+1) = 3 <> omega(29+1) + 3. So a(2) = 19.
Let i, p, b and w be the indices, the primes p_i, bigomega(p_i + 1) and omega(p_i + 1).
i: [ 1  2  3]
p: [19 23 29]
b: [ 3  4  3]
w: [ 2  2  3]
a(2) = 19
i: [  1   2   3   4]
p: [739 743 751 757]
b: [  4   5   5   2]
w: [  3   3   2   2]
a(3) = 739

Crossrefs

Cf. A001221, A001222, A072875, A086560, A369097, A373618.

Sequence in context: A355615 A329470 A107706 * A330040 A168591 A319190

Adjacent sequences: A373622 A373623 A373624 * A373627 A373628 A373629

Keyword

nonn,more

Author

Jean-Marc Rebert, Jun 11 2024

Status

approved