A214219 The least prime p such that sum(k=0...m, p^(k)) is divisible by m+1 for all m < n; where p^(k) denotes the k-th next larger prime: p^(0)=p, p^(1)=nextprime(p), etc.

2, 3, 3, 47, 1531, 4073, 5081, 537661, 5538947, 5981567, 148871869, 5545986967, 28511128379, 85185688439

Offset

1,1

Links

Table of n, a(n) for n=1..14.

C. Rivera (Ed.), Puzzle 415. Sets of consecutive primes such that... on primepuzzles.net.

Example

{47, 53, 59, 61} are 4 consecutive primes, 47+53 is a multiple of 2, 47+53+59 is a multiple of 3 and 47+53+59+61 is a multiple of 4. Since this is the least such set, a(4)=47.

Prog

(PARI) A214219(n)={ n<2 & return(2); my(p=vector(n, k, prime(k)), s=sum(k=1, n, p[k]), t);
for(i=0, 9e9, (s += -p[i%n+1] + p[i%n+1]=nextprime(p[(i-1)%n+1]+1))%n & next; (t=s-p[i%n+1])%(n-1) & next; for(j=2, n-2, (t -= p[(i-j+1)%n+1])%(n-j) & next(2)); return(p[(i+1)%n+1]))}

Crossrefs

Sequence in context: A101462 A345751 A242786 * A365223 A323340 A280895

Adjacent sequences: A214216 A214217 A214218 * A214220 A214221 A214222

Keyword

nonn

Author

M. F. Hasler, Jul 22 2012

Extensions

a(13)-a(14) from Jens Kruse Andersen, Jul 22 2012

Status

approved