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.

6639266409, 8628052209, 12692281897, 14492398389, 15798643881, 18883291565, 20404935965, 20825703713, 21342970293, 21597222381, 22221458853, 22567169229, 22578915665, 23000623161, 23198162685, 23247729109, 24163642653, 24802386189, 24894100941, 26297281109

Offset: 1

Author

Daniel Constantin Mayer, May 23 2014

Keywords

• nonn

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A242793 and A242804, A242805, A242806.

Programs

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
				

Extensions

More terms from Jens Kruse Andersen, Jun 18 2014