A073603 - OEIS

%I #19 Apr 21 2021 17:33:52

%S 4,6,15,56,66,52,153,323,552,435,186,370,861,1505,2068,2597,1770,671,

%T 3551,2556,949,4898,6142,1068,2425,5151,8240,5778,3052,1017,12446,

%U 14934,9453,18626,11175,3926,4239,20375,24048,25777,16110,3439,18336

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

%C If n is in A001359, a(n) = prime(n)*(prime(n)+1)/2. - _Robert Israel_, Apr 21 2021

%H Robert Israel, <a href="/A073603/b073603.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = prime(n)*A069830(n). - _Robert Israel_, Apr 21 2021

%e a(4) = 56 which is 8*7 and 56 ==1 (mod 11)

%p 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 # alternative

%p f:= (p,q)->(1/p mod q)*p:

%p seq(f(ithprime(i),ithprime(i+1)),i=1..100); # _Robert Israel_, Apr 21 2021

%t 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 Cf. A001359, A069830.

%K nonn,look

%O 1,1

%A _Amarnath Murthy_, Aug 04 2002

%E Corrected and extended by _Sascha Kurz_, Aug 10 2002