|
| |
|
|
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
|
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
|
|
|
|
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
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
