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Number of pairs of consecutive integers x, x+1 such that both are prime(n)-smooth but both are not prime(n-1)-smooth.
11

%I #25 Oct 15 2023 12:00:36

%S 1,3,6,13,17,28,40,59,74,104,137,171,216,284,349,428,524,652,790

%N Number of pairs of consecutive integers x, x+1 such that both are prime(n)-smooth but both are not prime(n-1)-smooth.

%C See A145605 for a triangle of x value. See A145606 for the largest x for each n.

%C An effective abc conjecture (c < rad(abc)^2) would imply that a(20)-a(33) is (943, 1201, 1401, 1738, 1955, 2240, 2793, 3340, 3860, 4582, 5284, 6050, 6883, 7984). - _Lucas A. Brown_, Oct 16 2022

%H Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/stormer.py">stormer.py</a>.

%Y Cf. A145605, A145606.

%Y First differences of A002071.

%K nonn,hard,more

%O 1,2

%A _T. D. Noe_, Oct 14 2008

%E a(16) from _Jean-François Alcover_, Nov 11 2016

%E a(17)-a(18) from _Lucas A. Brown_, Sep 20 2020

%E a(19) from _Lucas A. Brown_, Oct 16 2022