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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 (list; graph; refs; listen; history; text; internal format)
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 A245646

Adjacent sequences:  A250299 A250300 A250301 * A250303 A250304 A250305

KEYWORD

hard,more,nonn

AUTHOR

Don N. Page, Jan 15 2015

STATUS

approved

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Last modified October 28 16:09 EDT 2021. Contains 348329 sequences. (Running on oeis4.)