A157752 - OEIS

%I #20 May 04 2023 10:53:54

%S 2,8,68,1118,2273,197468,1728998,1728998,447914738,10152454583,

%T 1313795640428,97783391392958,5726413266646343,38433316595821418,

%U 15103232990013860963,943894249589930135768,52858423703753671390658,932521283899305953765183,8790842834979573009644273

%N Smallest positive integer m such that m == prime(i) (mod prime(i+1)) for all 1<=i<=n.

%C Suggested by Chinese Remainder Theorem.

%C a(n) is prime for n = 1, 5, 10, 23, 30.

%H Harvey P. Dale, <a href="/A157752/b157752.txt">Table of n, a(n) for n = 1..349</a>

%p A157752 := proc(n)

%p     local lrem,leval,i ;

%p     lrem := [] ;

%p     leval := [] ;

%p     for i from 1 to n do

%p         lrem := [op(lrem),ithprime(i+1)] ;

%p         leval := [op(leval),ithprime(i)] ;

%p     end do:

%p     chrem(leval,lrem) ;

%p end proc: # _R. J. Mathar_, Apr 14 2016

%t a[n_] := ChineseRemainder[Prime[Range[n]], Prime[Range[2, n + 1]]] a[ # ] & /@ Range[30]

%t Table[With[{pr=Prime[Range[n]]},ChineseRemainder[Most[pr],Rest[pr]]],{n,2,30}] (* _Harvey P. Dale_, Jun 11 2017 *)

%o (PARI) x=Mod(1, 1); for(i=1, 20, x=chinese(x, Mod(prime(i), prime(i+1))); print1(component(x, 2), ", "))

%o (Python)

%o from sympy.ntheory.modular import crt

%o from sympy import prime

%o def A157752(n): return int(crt((s:=[prime(i+1) for i in range(1,n)])+[prime(n+1)],[2]+s)[0]) # _Chai Wah Wu_, May 02 2023

%Y Cf. A053664, A071057, A121934.

%K nonn

%O 1,1

%A _Zak Seidov_, Mar 05 2009

%E Edited by _Charles R Greathouse IV_, Oct 28 2009