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.

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

Offset

1,1

Comments

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.

Links

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

Example

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.

Prog

(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

Crossrefs

Cf. A002072, A117581, A250298.

Sequence in context: A231212 A185174 A018695 * A156336 A078221 A376409

Adjacent sequences: A250299 A250300 A250301 * A250303 A250304 A250305

Keyword

hard,more,nonn

Author

Don N. Page, Jan 15 2015

Status

approved