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A073603 Smallest multiple of n-th prime which is == 1 mod (n+1)-st prime.

%I A073603 #19 Apr 21 2021 17:33:52
%S A073603 4,6,15,56,66,52,153,323,552,435,186,370,861,1505,2068,2597,1770,671,
%T A073603 3551,2556,949,4898,6142,1068,2425,5151,8240,5778,3052,1017,12446,
%U A073603 14934,9453,18626,11175,3926,4239,20375,24048,25777,16110,3439,18336
%N A073603 Smallest multiple of n-th prime which is == 1 mod (n+1)-st prime.
%C A073603 If n is in A001359, a(n) = prime(n)*(prime(n)+1)/2. - _Robert Israel_, Apr 21 2021
%H A073603 Robert Israel, <a href="/A073603/b073603.txt">Table of n, a(n) for n = 1..10000</a>
%F A073603 a(n) = prime(n)*A069830(n). - _Robert Israel_, Apr 21 2021
%e A073603 a(4) = 56 which is 8*7 and 56 ==1 (mod 11)
%p A073603 for i from 1 to 200 do a := msolve(ithprime(i)*n=1,ithprime(i+1)); b[i] := rhs(convert(a,list)[1])*ithprime(i); od:seq(b[k],k=1..200);
%p A073603 # alternative
%p A073603 f:= (p,q)->(1/p mod q)*p:
%p A073603 seq(f(ithprime(i),ithprime(i+1)),i=1..100); # _Robert Israel_, Apr 21 2021
%t A073603 p = 2; Table[q = NextPrime[p]; i = 2; While[Mod[y = i*p, q] != 1, i++]; p = q; y, {n, 43}] (* _Jayanta Basu_, Jul 02 2013 *)
%Y A073603 Cf. A001359, A069830.
%K A073603 nonn,look
%O A073603 1,1
%A A073603 _Amarnath Murthy_, Aug 04 2002
%E A073603 Corrected and extended by _Sascha Kurz_, Aug 10 2002