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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. 1
2, 3, 3, 47, 1531, 4073, 5081, 537661, 5538947, 5981567, 148871869, 5545986967, 28511128379, 85185688439 (list; graph; refs; listen; history; text; internal format)
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: A096502 A101462 A242786 * A088266 A116889 A037847

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

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Last modified December 19 18:59 EST 2014. Contains 252239 sequences.