A071373
Least number X such that the numbers from X to X+n-1 are, in some order, 1 * a prime, 2 * a prime, ..., n * a prime.
Original entry on oeis.org
2, 3, 4, 6, 6, 18362, 2914913, 10780552, 1829413731, 1676641682, 21487725800101, 22755817971366481, 107271326364325201, 7272877497848202226
Offset: 1
a(7)=2914913 because 2914913=1*2914913, 2914914=6*485819, 2914915=5*582983, 2914916=4*728729, 2914917=3*971639, 2914918=2*1457459 and 2914919=7*416417. The left factors are the integers 1 to 7; and the right factors are primes.
A071368
Numbers k such that k+0, k+1, k+2, k+3, k+4, and k+5 are, in some order, 1 * a prime, 2 * a prime, ... and 6 * a prime.
Original entry on oeis.org
18362, 2914913, 5516281, 6618242, 7224834, 9018353, 9339114, 10780554, 16831081, 17800553, 18164161, 18646202, 20239913, 29743561, 32464433, 32915513, 42464514, 43502033, 45652314, 51755761, 53464314, 62198634
Offset: 1
From _Reinhard Zumkeller_, Jul 31 2015: (Start)
18362 is in the sequence because 18362=2*9181, 18363=3*6121, 18364=4*4591, 18365=5*3673, 18366=6*3061 and 18367=1*18367. The left factors are the integers 1 to 6; and the right factors are primes.
5516281 is the smallest term also occurring in A071367:
5516281 + 0 = 1 * 5516281 = prime(381844) = a(3) = A071367(77);
5516281 + 1 = 2 * 2758141 = 2 * prime(200537);
5516281 + 2 = 3 * 1838761 = 3 * prime(137758);
5516281 + 3 = 4 * 1379071 = 4 * prime(105622);
5516281 + 4 = 5 * 1103257 = 5 * prime(85955);
5516281 + 5 = 6 * 919381 = 6 * prime(72692), not needed for A071367.
(End)
-
a071368 n = a071368_list !! (n-1)
a071368_list = filter f [1..] where
f x = and $ map g [6, 5 .. 1] where
g k = sum (map h $ map (+ x) [0..5]) == 1 where
h z = if r == 0 then a010051' z' else 0
where (z', r) = divMod z k
-- Reinhard Zumkeller, Jul 31 2015
A071369
Numbers n such that n+0, n+1, ... and n+6 are, in some order, 1 * a prime, 2 * a prime, ... and 7 * a prime.
Original entry on oeis.org
2914913, 5516281, 6618241, 9018353, 10780553, 18164161, 20239913, 45652313, 51755761, 62198633, 81235441, 91986833, 158764313, 175472641, 191010953, 197375753, 215206201, 322030801, 322461713, 362007353, 513284401, 668745001
Offset: 1
2914913 is there because 2914913=1*2914913, 2914914=6*485819, 2914915=5*582983, 2914916=4*728729, 2914917=3*971639, 2914918=2*1457459 and 2914919=7*416417. The left factors are the integers 1 to 7; and the right factors are primes.
A071370
Numbers n such that n+0, n+1, ... and n+7 are, in some order, 1 * a prime, 2 * a prime, ... and 8 * a prime.
Original entry on oeis.org
10780552, 62198632, 884811061, 1457032501, 3573315892, 7321991041, 7391371681, 8557865812, 11434075381, 16893247141, 21599190901, 22487905441, 28044279892, 28273111012, 37923188932, 50238568801, 59635316161
Offset: 1
10780552 is there because 10780552=8*1347569, 10780553=7*1540079, 10780554=6*1796759, 10780555=5*2156111, 10780556=4*2695139, 10780557=3*3593519, 10780558=2*5390279 and 10780559=1*10780559. The left factors are the integers 1 to 8; and the right factors are primes.
A071372
Numbers n such that n+0, n+1, ... and n+9 are, in some order, 1 * a prime, 2 * a prime, ... and 10 * a prime.
Original entry on oeis.org
1676641682, 1829413730, 862353305089, 2394196081201, 7816812203762, 9089234694530, 10689865119781, 10988437006262, 13826845745989, 17242727247890, 21487725800102, 24653435773682, 28779837186662
Offset: 1
1676641682 is there because 1676641682=2*838320841, 1676641683=3*558880561, 1676641684=4*419160421, 1676641685=5*335328337, 1676641686=6*279440281, 1676641687=7*239520241, 1676641688=8*209580211, 1676641689=9*186293521, 1676641690=10*167664169 and 1676641691=1*1676641691. The left factors are the integers 1 to 10; and the right factors are primes.
A071371
Numbers n such that n+0, n+1, ... and n+8 are, in some order, 1 * a prime, 2 * a prime, ... and 9 * a prime.
Original entry on oeis.org
1829413731, 13096880161, 28273111011, 32480018341, 79089694311, 330780346261, 363500177041, 602794125781, 679251409201, 905780175301, 956731265701, 1010903523841, 1011470714101, 1086338816631, 1312670706051
Offset: 1
1829413731 is there because 1829413731=3*609804577, 1829413732=4*457353433, 1829413733=7*261344819, 1829413734=6*304902289, 1829413735=5*365882747, 1829413736=8*228676717, 1829413737=9*203268193, 1829413738=2*914706869 and 1829413739=1*1829413739. The left factors are the integers 1 to 9; and the right factors are primes.
Showing 1-6 of 6 results.
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