cp's OEIS Frontend

A157752 Smallest positive integer m such that m == prime(i) (mod prime(i+1)) for all 1<=i<=n.

%I A157752 #20 May 04 2023 10:53:54
%S A157752 2,8,68,1118,2273,197468,1728998,1728998,447914738,10152454583,
%T A157752 1313795640428,97783391392958,5726413266646343,38433316595821418,
%U A157752 15103232990013860963,943894249589930135768,52858423703753671390658,932521283899305953765183,8790842834979573009644273
%N A157752 Smallest positive integer m such that m == prime(i) (mod prime(i+1)) for all 1<=i<=n.
%C A157752 Suggested by Chinese Remainder Theorem.
%C A157752 a(n) is prime for n = 1, 5, 10, 23, 30.
%H A157752 Harvey P. Dale, <a href="/A157752/b157752.txt">Table of n, a(n) for n = 1..349</a>
%p A157752 A157752 := proc(n)
%p A157752     local lrem,leval,i ;
%p A157752     lrem := [] ;
%p A157752     leval := [] ;
%p A157752     for i from 1 to n do
%p A157752         lrem := [op(lrem),ithprime(i+1)] ;
%p A157752         leval := [op(leval),ithprime(i)] ;
%p A157752     end do:
%p A157752     chrem(leval,lrem) ;
%p A157752 end proc: # _R. J. Mathar_, Apr 14 2016
%t A157752 a[n_] := ChineseRemainder[Prime[Range[n]], Prime[Range[2, n + 1]]] a[ # ] & /@ Range[30]
%t A157752 Table[With[{pr=Prime[Range[n]]},ChineseRemainder[Most[pr],Rest[pr]]],{n,2,30}] (* _Harvey P. Dale_, Jun 11 2017 *)
%o A157752 (PARI) x=Mod(1, 1); for(i=1, 20, x=chinese(x, Mod(prime(i), prime(i+1))); print1(component(x, 2), ", "))
%o A157752 (Python)
%o A157752 from sympy.ntheory.modular import crt
%o A157752 from sympy import prime
%o A157752 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 A157752 Cf. A053664, A071057, A121934.
%K A157752 nonn
%O A157752 1,1
%A A157752 _Zak Seidov_, Mar 05 2009
%E A157752 Edited by _Charles R Greathouse IV_, Oct 28 2009