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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.
0
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.
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
KEYWORD
hard,more,nonn
AUTHOR
Don N. Page, Jan 15 2015
STATUS
approved