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

4, 6, 15, 56, 66, 52, 153, 323, 552, 435, 186, 370, 861, 1505, 2068, 2597, 1770, 671, 3551, 2556, 949, 4898, 6142, 1068, 2425, 5151, 8240, 5778, 3052, 1017, 12446, 14934, 9453, 18626, 11175, 3926, 4239, 20375, 24048, 25777, 16110, 3439, 18336

Offset: 1

Author

Amarnath Murthy, Aug 04 2002

Keywords

• nonn
• look

Comments

If n is in A001359, a(n) = prime(n)*(prime(n)+1)/2. - Robert Israel, Apr 21 2021

Examples

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

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001359, A069830.

Programs

Maple

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);
# alternative
f:= (p,q)->(1/p mod q)*p:
seq(f(ithprime(i),ithprime(i+1)),i=1..100); # Robert Israel, Apr 21 2021

Mathematica

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 *)

Formula

a(n) = prime(n)*A069830(n). - Robert Israel, Apr 21 2021

Extensions

Corrected and extended by Sascha Kurz, Aug 10 2002