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A214219
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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.
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1
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2, 3, 3, 47, 1531, 4073, 5081, 537661, 5538947, 5981567, 148871869, 5545986967, 28511128379, 85185688439
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OFFSET
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1,1
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LINKS
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EXAMPLE
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{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.
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PROG
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(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]))}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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