

A073607


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


7



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
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OFFSET

1,1


COMMENTS

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


LINKS

Table of n, a(n) for n=1..52.


EXAMPLE

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.


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} ]


CROSSREFS

Cf. A073606, A072555, A073754, A073755, A073756 & A072562.
Sequence in context: A272738 A272782 A272805 * A086062 A006416 A273069
Adjacent sequences: A073604 A073605 A073606 * A073608 A073609 A073610


KEYWORD

nonn


AUTHOR

Amarnath Murthy, Aug 04 2002


EXTENSIONS

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


STATUS

approved



