A073606 Smaller of two consecutive integers divisible respectively by two consecutive primes.

2, 8, 9, 14, 20, 21, 24, 26, 32, 38, 39, 44, 50, 54, 55, 56, 62, 68, 69, 74, 77, 80, 84, 86, 90, 92, 98, 99, 104, 110, 114, 115, 116, 122, 125, 128, 129, 134, 140, 144, 146, 152, 158, 159, 160, 164, 169, 170, 174, 175, 176, 182, 188, 189, 194, 195, 200, 204, 206

Offset: 1

Author

Amarnath Murthy, Aug 04 2002

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A073755, A073607, A072555, A073754, A073756, A072562.

Programs

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, 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} ]
npQ[n_] := Or @@ Divisible[n + 1, NextPrime[First /@ FactorInteger[n]]]; Select[Range[2, 210], npQ[#] &] (* Jayanta Basu, Jul 03 2013 *)

Extensions

Edited by Robert G. Wilson v, Aug 07 2002