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A072730
Smallest of 5 consecutive integers divisible respectively by 5 consecutive primes.
1
788, 789, 3098, 5408, 7718, 10028, 12338, 14648, 15804, 16958, 19268, 21578, 23888, 26198, 28508, 30818, 30819, 33128, 35438, 37748, 40058, 40830, 42368, 44678, 45834, 46988, 49298, 51608, 53918, 56228, 58538, 60848, 60849, 63158
OFFSET
1,1
LINKS
EXAMPLE
3098 is a term as 3098, 3099, 3100, 3101 and 3102 are divisible by 2, 3, 5, 7 and 11 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, 4} ]; k = 1; While[ k < l + 1 && Union[ Mod[ t, NestList[ NextPrim, p[[ k ]], 4 ]]] != {0}, k++ ]; If[ k < l + 1, Print[ n ]], {n, 2, 72397} ]
cicpQ[n_]:=Module[{num=Range[n, n+4], pr=PrimePi[n+4]-4}, Total [Boole[ AllTrue[ #, IntegerQ]&/@Table[num/Prime[Range[k, k+4]], {k, pr}]]]>0]; Select[ Range[ 64000], cicpQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 11 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Aug 07 2002
STATUS
approved