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%I #14 Mar 23 2021 05:20:24
%S 2,8,9,14,20,21,24,26,32,38,39,44,50,54,55,56,62,68,69,74,77,80,84,86,
%T 90,92,98,99,104,110,114,115,116,122,125,128,129,134,140,144,146,152,
%U 158,159,160,164,169,170,174,175,176,182,188,189,194,195,200,204,206
%N Smaller of two consecutive integers divisible respectively by two consecutive primes.
%C There are arbitrarily long strings of consecutive integers in this sequence; for example, A072562(k+1) is followed by at least k-1 more consecutive members. - _David Wasserman_, Oct 21 2004
%H Amiram Eldar, <a href="/A073606/b073606.txt">Table of n, a(n) for n = 1..10000</a>
%e 54 is a term as 54 and 55 are divisible by 3 and 5 respectively. 55 is also a term as 55 and 56 are divisible by 5 and 7. 56 is also a term as 56 and 57 are divisible by 2 and 3.
%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, 1} ]; k = 1; While[ k < l + 1 && Union[ Mod[ t, NestList[ NextPrim, p[[ k ]], 1 ]]] != {0}, k++ ]; If[ k < l + 1, Print[ n ]], {n, 2, 220} ]
%t npQ[n_] := Or @@ Divisible[n + 1, NextPrime[First /@ FactorInteger[n]]]; Select[Range[2, 210], npQ[#] &] (* _Jayanta Basu_, Jul 03 2013 *)
%Y Cf. A073755, A073607, A072555, A073754, A073756, A072562.
%K nonn
%O 1,1
%A _Amarnath Murthy_, Aug 04 2002
%E Edited by _Robert G. Wilson v_, Aug 07 2002
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