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A073607
Smallest of three consecutive integers divisible by three consecutive primes respectively.
8
8, 20, 38, 54, 68, 98, 114, 128, 158, 159, 169, 188, 218, 248, 264, 278, 308, 338, 368, 369, 398, 405, 428, 458, 474, 488, 518, 548, 578, 579, 608, 638, 668, 684, 698, 728, 758, 788, 789, 790, 791, 818, 848, 878, 894, 908, 938, 968, 998, 999, 1028, 1058
OFFSET
1,1
COMMENTS
The sequence is infinite as 30*k + 8 is a member for all k. What is the longest string of consecutive integers?
LINKS
EXAMPLE
20 is a term as 20,21 and 22 are divisible by 5,7 and 11 respectively.
114 is a term as 114, 115 and 116 are divisible by 19, 23 and 29 respectively.
MATHEMATICA
f[ n_Integer ] := Flatten[ Table[ #1 ] & @@@ FactorInteger[ n ]]; NextPrim[ n_ ] := Block[ {k = n + 1}, While[ !PrimeQ[ k ], k++ ]; k ]; Do[ p = f[ n ]; l = Length[ p ]; t = Table[ n + i, {i, 0, 2} ]; k = 1; While[ k < l + 1 && Union[ Mod[ t, NestList[ NextPrim, p[[ k ]], 2 ] ]] != {0}, k++ ]; If[ k < l + 1, Print[ n ]], {n, 2, 1117} ]
CROSSREFS
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Aug 04 2002
EXTENSIONS
Edited, corrected and extended by Robert G. Wilson v, Aug 06 2002
STATUS
approved