

A116486


Numbers n such that both n and n+1 are logarithmically smooth.


3



8, 24, 80, 125, 224, 2400, 3024, 4224, 4374, 6655, 9800, 10647, 123200, 194480, 336140, 601425, 633555, 709631, 5142500, 5909760, 11859210, 1611308699
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OFFSET

1,1


COMMENTS

N is logarithmically smooth if its largest prime factor is <= ceil(log2(n)).
Is the sequence finite?
No more terms with largest prime factor <= 47. [Joerg Arndt, Jul 02 2012]


LINKS

Table of n, a(n) for n=1..22.
Discussion titled Special Smooth numbers, (postings in mersenneforum.org), starting March 20 2006.


EXAMPLE

125 is there because 125=5*5*5, 126=2*3*3*7; no prime factor is greater than ceiling(log2(125))=7.


PROG

(PARI)
fm=97; /* max factor for factorizing, 2^97 >= searchlimit */
lpf(n)={ vecmax(factor(n, fm)[, 1]) } /* largest prime factor */
lsm(n)=if ( lpf(n)<=#binary(n1), 1, 0 ); /* whether logsmooth, for n>=2 */
n0=3; /* lower search limit */
l1=lsm(n01);
{ for (n=n0, 10^10,
l0 = lsm(n);
if ( l0 && l1, print1(n1, ", ") );
l1 = l0;
); }
/* Joerg Arndt, Jul 02 2012 */


CROSSREFS

Sequence in context: A303402 A078158 A221906 * A179609 A241690 A141317
Adjacent sequences: A116483 A116484 A116485 * A116487 A116488 A116489


KEYWORD

nonn,hard,more


AUTHOR

Harsh R. Aggarwal, Mar 20 2006


EXTENSIONS

Edited by Don Reble, Apr 07 2006


STATUS

approved



