A145606 Largest number x such that x and x+1 are prime(n)-smooth but not prime(n-1)-smooth.

1, 8, 80, 4374, 9800, 123200, 336140, 11859210, 5142500, 177182720, 1611308699, 3463199999, 63927525375, 421138799639, 1109496723125, 1453579866024, 20628591204480, 31887350832896, 12820120234375, 119089041053696, 2286831727304144, 9591468737351909375, 17451620110781856, 166055401586083680, 49956990469100000, 4108258965739505499, 19316158377073923834000, 386539843111191224

Offset: 1

Author

T. D. Noe, Oct 14 2008

Keywords

• nonn
• hard

Comments

Note that this sequence is not always increasing. For many n, a(n) is the same as A002072(n). See A145605 for a triangle of values.

An effective abc conjecture (c < rad(abc)^2) would imply that a(29)-a(33) is (90550606380841216610, 205142063213188103639, 53234795127882729824, 4114304445616636016031, 124225935845233319439173). - Lucas A. Brown, Sep 20 2020

Links

• Jim White, Results to P = 127

Crossrefs

Cf. A002072, A117581, A145605, A175607.

Extensions

Terms a(16) onward by Andrey V. Kulsha, Aug 10 2011, according to Jim White's computations