proposed

approved

editing

proposed

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.

114 is a term as 114, 115 and 116 are divisible by 19, 23 and 29 respectively.

proposed

editing

editing

proposed

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

Amiram Eldar, <a href="/A073607/b073607.txt">Table of n, a(n) for n = 1..10000</a>

Cf. A073606, A072555, A073754, A073755, A073756 & , A072562.

approved

editing

_Amarnath Murthy (amarnath_murthy(AT)yahoo.com), _, Aug 04 2002

Edited, corrected and extended by _Robert G. Wilson v (rgwv(AT)rgwv.com), _, Aug 06 2002

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} ]

nonn,new

nonn

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

1,1

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

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.

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} ]

Cf. A073606, A072555, A073754, A073755, A073756 & A072562.

nonn

Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Aug 04 2002

Edited, corrected and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 06 2002

approved