A234423 a(n) = the smallest multiple of prime(n) such that a(n) == j-1 (mod j) for each integer j with 1 <= j < prime(n).

2, 3, 35, 119, 2519, 277199, 5045039, 183783599, 4655851199, 80313433199, 32607253879199, 2743667504978399, 58772246027695199, 5038384364010597599

Offset: 1

Author

Jaroslav Krizek, Dec 25 2013

Keywords

• nonn

Comments

Sequence of numbers k(n): 1, 1, 7, 17, 229, 21323, 296767, 9672821, 202428313, 2769428731, 1051846899329, ...

Examples

			Prime(4) = 7, a(4) = 119 = 7*17 because 119 is smallest multiple of 7 such that 119 mod 1 = 0, 119 mod 2 = 1, 119 mod 3 = 2, 119 mod 4 = 3, 119 mod 5 = 4, 119 mod 6 = 5.
		

Crossrefs

Cf. A000040 (primes), A094998.

Programs

PARI

for(n=1, 10, p=prime(n); forstep(m=p, 10^11, p, forstep(j=p-1, 1, -1, if(m%j<>j-1, next(2))); print(n " " m); next(2))) \\ Donovan Johnson, Dec 30 2013

Extensions

a(12)-a(14) from Donovan Johnson, Dec 30 2013