

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
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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 nth 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(1k, 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



