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Smallest of 7 consecutive integers divisible respectively by 7 consecutive primes.
1

%I #7 Mar 23 2021 05:20:29

%S 210998,466254,721508,1232018,1742528,2253038,2763548,3274058,3784568,

%T 4295078,4805588,5316098,5316099,5826608,6337118,6847628,7358138,

%U 7868648,8379158,8889668,9400178,9910688,10165944,10421198,10931708

%N Smallest of 7 consecutive integers divisible respectively by 7 consecutive primes.

%H Amiram Eldar, <a href="/A072760/b072760.txt">Table of n, a(n) for n = 1..10000</a>

%e 210998 is a term as 210998, 210999, 211000, 211001, 211002, 211003 and 211004 are divisible by 2, 3, 5, 7, 11, 13 and 17 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, 6} ]; k = 1; While[ k < l + 1 && Union[ Mod[ t, NestList[ NextPrim, p[[ k ]], 6 ]]] != {0}, k++ ]; If[ k < l + 1, Print[ n ]], {n, 2, 811597} ]

%Y Cf. A073606, A073607, A072555, A073754, A073755, A072562.

%K nonn

%O 1,1

%A _Robert G. Wilson v_, Aug 08 2002