A073607 Smallest of three consecutive integers divisible by three consecutive primes respectively.

8, 20, 38, 54, 68, 98, 114, 128, 158, 159, 169, 188, 218, 248, 264, 278, 308, 338, 368, 369, 398, 405, 428, 458, 474, 488, 518, 548, 578, 579, 608, 638, 668, 684, 698, 728, 758, 788, 789, 790, 791, 818, 848, 878, 894, 908, 938, 968, 998, 999, 1028, 1058

Offset: 1

Author

Amarnath Murthy, Aug 04 2002

Keywords

• nonn

Comments

The sequence is infinite as 30*k + 8 is a member for all k. What is the longest string of consecutive integers?

Examples

			20 is a term as 20,21 and 22 are divisible by 5,7 and 11 respectively.
114 is a term as 114, 115 and 116 are divisible by 19, 23 and 29 respectively.
		

Links

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

Crossrefs

Cf. A073606, A072555, A073754, A073755, 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, 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} ]

Extensions

Edited, corrected and extended by Robert G. Wilson v, Aug 06 2002