OFFSET
1,2
COMMENTS
Suggested by Chinese Remainder Theorem.
REFERENCES
Niven and Zuckerman, An Introduction to the Theory of Numbers, John Wiley, 1966, p. 40
Paulo Ribenboim, The New Book of Prime Numbers Records, Springer 1996, p. 33
LINKS
Nick Hobson and Robert G. Wilson v, Table of n, a(n) for n = 1..350 (first 100 terms from Nick Hobson)
Project Euler, Problem 552: Chinese leftovers II
EXAMPLE
a(3) = 23 because this is the smallest number m such that m == 1 (mod 2), m == 2 (mod 3) and m == 3 (mod 5).
a(4) = 53 because 53 - 1 is divisible by 2, 53 - 2 is divisible by 3, 53 - 3 is divisible by 5 and 53 - 4 is divisible by 7.
MATHEMATICA
f[n_] := ChineseRemainder[ Range[n], Prime[Range[n]]]; Array[f, 20]
PROG
(PARI) for(n=1, 20, m=1; while(sum(i=1, n, abs(m%prime(i)-i))>0, m++); print1(m, ", "))
(PARI) x=Mod(1, 1); for(i=1, 18, x=chinese(x, Mod(i, prime(i))); print1(component(x, 2), ", ")) /* Nick Hobson (nickh(AT)qbyte.org), Jan 08 2007 */
(Python)
from sympy.ntheory.modular import crt
from sympy import prime
def A053664(n): return int(crt([prime(i) for i in range(1, n+1)], list(range(1, n+1)))[0]) # Chai Wah Wu, May 01 2023
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
Joe K. Crump (joecr(AT)carolina.rr.com), Feb 16 2000
EXTENSIONS
Additional comments from Luis A. Rodriguez (luiroto(AT)yahoo.com), Apr 23 2002
Edited by N. J. A. Sloane and Robert G. Wilson v, May 03 2002
STATUS
approved