A367063 Least number k such that there exists a subset u of n distinct elements of {1..k} for which Sum_{i = 1..n} u(i) * prime(u(i)) mod Sum_{i = 1..n} u(i) = 0.

1, 4, 5, 6, 7, 8, 9, 9, 12, 13, 14, 15, 16, 16, 18, 18, 19, 20, 22, 22, 23, 24, 25, 27, 28, 28, 30, 30, 31, 33, 33, 34, 35, 37, 38, 39, 40, 40, 41, 42, 44, 44, 45, 46, 48, 49, 50, 51, 52, 52, 53, 55, 55, 56, 58, 59, 59, 60, 62, 61, 63, 64, 66, 67, 67, 67, 69, 70

Offset

1,2

Links

Table of n, a(n) for n=1..68.

Example

a(1) = 1, because 1*prime(1) mod 1 = 2 mod 1 = 0 and no lesser number has this property.
a(2) = 4, because 1*prime(1) + 4*prime(4) mod (1+4) = 30 mod 5 = 0 and no lesser number has this property.

Prog

(PARI) is(u)=my(v=vector(#u, x, prime(u[x]))); my(r=u*v~%vecsum(u)); if(r==0, 1, 0)
find(k, n)=forsubset([k, n], s, my(u=Vec(s)); if(is(u), return(k))); 0
a(n)=my(k=n, u=find(k, n)); while(u==0, k++; u=find(k, n)); k

Crossrefs

Sequence in context: A090925 A143836 A168094 * A089166 A178052 A030543

Adjacent sequences: A367060 A367061 A367062 * A367064 A367065 A367066

Keyword

nonn

Author

Jean-Marc Rebert, Nov 04 2023

Status

approved