cp's OEIS Frontend

A250302 Positive integers k whose square is, for some prime p, the largest integer m such that both m and m-1 factor into primes less than or equal to p.

%I A250302 #17 Mar 20 2015 21:03:55
%S A250302 3,9,99,351,13311,1205645,138982582999
%N A250302 Positive integers k whose square is, for some prime p, the largest integer m such that both m and m-1 factor into primes less than or equal to p.
%C A250302 a(n)^2-1 and a(n)^2 form the largest pair of consecutive p-smooth numbers.
%C A250302 Terms are the square roots of square values of A117581(=A002072+1).
%C A250302 The corresponding primes p are in A250298.
%e A250302 Here are the largest pairs of consecutive integers with prime factors p or smaller:
%e A250302 p   : pair
%e A250302 --------------------------
%e A250302 3   : 3^2-1 and 3^2;
%e A250302 5   : 9^2-1 and 9^2;
%e A250302 11  : 99^2-1 and 99^2;
%e A250302 13  : 351^2-1 and 351^2;
%e A250302 29  : 13311^2-1 and 13311^2;
%e A250302 53  : 1205645^2-1 and 1205645^2;
%e A250302 103 : 138982582999^2-1 and 138982582999^2.
%o A250302 (PARI) lista(v_002072) = {v = v_002072; for (i=1, #v, vi = v[i]; if (issquare(vi+1), print1(sqrtint(vi+1), ", ")););} \\ _Michel Marcus_, Feb 28 2015
%Y A250302 Cf. A002072, A117581, A250298.
%K A250302 hard,more,nonn
%O A250302 1,1
%A A250302 _Don N. Page_, Jan 15 2015