

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
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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



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


STATUS

approved



