A250298 -id:A250298 - cp's OEIS frontend

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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.

Original entry on oeis.org

3, 9, 99, 351, 13311, 1205645, 138982582999

Offset: 1

Don N. Page, Jan 15 2015

a(n)^2-1 and a(n)^2 form the largest pair of consecutive p-smooth numbers.
Terms are the square roots of square values of A117581(=A002072+1).
The corresponding primes p are in A250298.

			Here are the largest pairs of consecutive integers with prime factors p or smaller:
p   : pair
--------------------------
3   : 3^2-1 and 3^2;
5   : 9^2-1 and 9^2;
11  : 99^2-1 and 99^2;
13  : 351^2-1 and 351^2;
29  : 13311^2-1 and 13311^2;
53  : 1205645^2-1 and 1205645^2;
103 : 138982582999^2-1 and 138982582999^2.

Cf. A002072, A117581, A250298.

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

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