A100572 Largest prime p such that the sum of n consecutive primes plus p is equal to (n+1)^3.

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

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: A125202 A024841 A155737 * 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