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%I #9 Mar 23 2021 05:20:11
%S 8,20,38,54,68,98,114,128,158,159,169,188,218,248,264,278,308,338,368,
%T 369,398,405,428,458,474,488,518,548,578,579,608,638,668,684,698,728,
%U 758,788,789,790,791,818,848,878,894,908,938,968,998,999,1028,1058
%N Smallest of three consecutive integers divisible by three consecutive primes respectively.
%C The sequence is infinite as 30*k + 8 is a member for all k. What is the longest string of consecutive integers?
%H Amiram Eldar, <a href="/A073607/b073607.txt">Table of n, a(n) for n = 1..10000</a>
%e 20 is a term as 20,21 and 22 are divisible by 5,7 and 11 respectively.
%e 114 is a term as 114, 115 and 116 are divisible by 19, 23 and 29 respectively.
%t 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} ]
%Y Cf. A073606, A072555, A073754, A073755, A073756, A072562.
%K nonn
%O 1,1
%A _Amarnath Murthy_, Aug 04 2002
%E Edited, corrected and extended by _Robert G. Wilson v_, Aug 06 2002
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