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A100572 Largest prime p such that the sum of n consecutive primes plus p is equal to (n+1)^3. 1
5, 19, 41, 89, 163, 271, 19, 631, 677, 1103, 1237, 1879, 2053, 3049, 3299, 4229, 5333, 5857, 7219, 7607, 9859, 11117, 12577, 14173, 16417, 16223, 20477, 22679, 25409, 26833, 30509, 32771, 36887, 39989, 43759, 47911, 52127, 56237, 60013, 65657, 69691, 74887 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Does a(n) exist for each n? - Charles R Greathouse IV, Jun 03 2013

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

EXAMPLE

a(2)=19 because 3+5+19=3^3;

a(3)=41 because 5+7+11+41=4^3;

a(4)=89 because 5+7+11+13+89=5^3.

PROG

(PARI) a(n)=if(n==1, return(5)); my(v=primes(n), s=sum(i=1, n, v[i]), N=(n+1)^3); forprime(p=v[#v]+1, N, if(isprime(N-s), return(N-s)); if(N<s, return(-1)); s+=p-v[1]; v=concat(v[2..n], p)) \\ Charles R Greathouse IV, Jun 03 2013

CROSSREFS

Sequence in context: A024841 A155737 A140761 * A119534 A306190 A033622

Adjacent sequences:  A100569 A100570 A100571 * A100573 A100574 A100575

KEYWORD

nonn

AUTHOR

Giovanni Teofilatto, Nov 29 2004

EXTENSIONS

a(7) inserted, a(9)-a(42) from Charles R Greathouse IV, Jun 03 2013

STATUS

approved

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Last modified March 23 04:46 EDT 2019. Contains 321422 sequences. (Running on oeis4.)