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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 (list; graph; refs; listen; history; text; internal format)
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(n-1), 1, 0 );  /* whether log-smooth, for n>=2 */

n0=3;  /* lower search limit */

l1=lsm(n0-1);

{ for (n=n0, 10^10,

    l0 = lsm(n);

    if ( l0 && l1, print1(n-1, ", ") );

    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

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Last modified October 19 13:01 EDT 2019. Contains 328222 sequences. (Running on oeis4.)