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A069561 Start of a run of n consecutive positive numbers divisible respectively by first n primes. 5
2, 2, 8, 158, 788, 788, 210998, 5316098, 34415168, 703693778, 194794490678, 5208806743928, 138782093170508, 5006786309605868, 253579251611336438, 12551374903381164638, 142908008812141343558, 77053322014980646906358 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

It is evident that from a(3) onwards terms must be congruent to 8 mod p(3)#, where p(n)# is the n-th primorial (A002110). In fact the sequence for A069561(n) == k (mod p(n)#) for k: 2, 2, 8, 788, 788, 210988, etc. This follows from the Chinese Remainder Theorem.

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..350

FORMULA

log a(n) << n log n. - Charles R Greathouse IV, Jun 20 2015

EXAMPLE

a(5) = 788 as 788, 789, 790, 791 and 792 are divisible by 2, 3, 5, 7, and 11 respectively.

MATHEMATICA

f[n_] := ChineseRemainder[-Range[0, n - 1], Prime[Range[n]]]; Array[f, 17, 2] (* Robert G. Wilson v, Jan 13 2012 *)

PROG

(PARI) a(n)=lift(chinese(vector(max(n, 2), k, Mod(1-k, prime(k))))) \\ Charles R Greathouse IV, Jun 20 2015

CROSSREFS

Cf. A072562.

Sequence in context: A270405 A047692 A270316 * A180370 A011148 A176020

Adjacent sequences:  A069558 A069559 A069560 * A069562 A069563 A069564

KEYWORD

nonn

AUTHOR

Amarnath Murthy, Mar 22 2002

EXTENSIONS

More terms to a(15) from Sascha Kurz, Mar 23 2002

Edited and extended by Robert G. Wilson v, Aug 09 2002

STATUS

approved

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Last modified July 21 04:27 EDT 2017. Contains 289632 sequences.