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A242829 Integers n such that each of n, n+1, n+2, n+4, n+5, n+6 is the squarefree product of five primes. 4
6639266409, 8628052209, 12692281897, 14492398389, 15798643881, 18883291565, 20404935965, 20825703713, 21342970293, 21597222381, 22221458853, 22567169229, 22578915665, 23000623161, 23198162685, 23247729109, 24163642653, 24802386189, 24894100941, 26297281109 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This is a higher analog to A242804, A242805, A242806.

It is very tough to compute this sequence on a single machine. Therefore, the interval from 0 to 9*10^9 was subdivided into 9 partial intervals, of length 10^9 each, and scanned by different computers. Nevertheless the CPU time was extrapolated for a single machine and summed up to 30 hours for the first member 6639266409 and 47 hours (~2 days) for the second member 8628052209. Up to 10^10, there is no occurrence of a next term.

LINKS

Jens Kruse Andersen, Table of n, a(n) for n = 1..195

EXAMPLE

a(1) = 6639266409 =  3 * 29 * 109 * 421 *   1663,

       6639266410 =  2 *  5 *   7 * 113 * 839351,

       6639266411 = 17 * 23 *  89 * 101 *   1889,

       6639266413 = 13 * 61 *  79 * 131 *    809,

       6639266414 =  2 * 11 * 349 * 857 *   1009,

       6639266415 =  3 *  5 *  73 * 149 *  40693;

and

a(2) = 8628052209 =  3 *  7 *  19 * 863 *  25057,

       8628052210 =  2 *  5 * 251 * 953 *   3607,

       8628052211 = 17 * 43 * 179 * 233 *    283,

       8628052213 = 11 * 47 * 127 * 331 *    397,

       8628052214 =  2 * 53 * 107 * 131 *   5807,

       8628052215 =  3 *  5 *  23 *  31 * 806737.

PROG

(PARI)

{ default(primelimit, 1000M); i=0; j=0; k=0; l=0; m=0; loc=0; lb=2; ub=9*10^9; o=5; for(n=lb, ub, if(issquarefree(n)&&(o==omega(n)), loc=loc+1; if(1==loc, i=n; ); if(2==loc, if(i+1==n, j=n; ); if(i+1<n, loc=1; i=n; ); ); if(3==loc, if(j+1==n, k=n; ); if(j+1<n, loc=1; i=n; ); ); if(4==loc, if(k+2==n, l=n; ); if(k+2<n, loc=1; i=n; ); ); if(5==loc, if(l+1==n, m=n; ); if(l+1<n, loc=1; i=n; ); ); if(6==loc, if(m+1==n, print1(i, ", "); loc=0; ); if(m+1<n, loc=1; i=n; ); ); ); ); }

CROSSREFS

Cf. A242793 and A242804, A242805, A242806.

Sequence in context: A127342 A268845 A161160 * A233502 A113640 A233623

Adjacent sequences:  A242826 A242827 A242828 * A242830 A242831 A242832

KEYWORD

nonn

AUTHOR

Daniel Constantin Mayer, May 23 2014

EXTENSIONS

More terms from Jens Kruse Andersen, Jun 18 2014

STATUS

approved

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Last modified November 19 08:57 EST 2018. Contains 317348 sequences. (Running on oeis4.)