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A053664 Smallest number m such that m == i (mod prime(i)) for all 1<=i<=n. 14
1, 5, 23, 53, 1523, 29243, 299513, 4383593, 188677703, 5765999453, 5765999453, 2211931390883, 165468170356703, 8075975022064163, 361310530977154973, 20037783573808880093, 1779852341342071295513, 40235059344426324076913 (list; graph; refs; listen; history; text; internal format)
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)
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
Cf. A192363.
Sequence in context: A289154 A155851 A019267 * A186030 A092544 A319087
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

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Last modified May 19 20:45 EDT 2024. Contains 372703 sequences. (Running on oeis4.)