The On-Line Encyclopedia of Integer Sequences (OEIS)

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A100572

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

#8 by Joerg Arndt at Mon Jun 03 14:05:55 EDT 2013

STATUS

proposed

approved

#7 by Charles R Greathouse IV at Mon Jun 03 14:04:05 EDT 2013

STATUS

editing

proposed

#6 by Charles R Greathouse IV at Mon Jun 03 14:03:59 EDT 2013

EXTENSIONS

a(7) corrected, inserted, a(89)-a(42) from Charles R Greathouse IV, Jun 03 2013

#5 by Charles R Greathouse IV at Mon Jun 03 14:03:20 EDT 2013

NAME

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

DATA

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

COMMENTS

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

LINKS

Charles R Greathouse IV, <a href="/A100572/b100572.txt">Table of n, a(n) for n = 1..10000</a>

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

EXTENSIONS

a(7) corrected, a(8)-a(42) from Charles R Greathouse IV, Jun 03 2013

STATUS

proposed

editing

#4 by Michel Marcus at Mon Jun 03 12:36:37 EDT 2013

STATUS

editing

proposed

#3 by Michel Marcus at Mon Jun 03 12:36:33 EDT 2013

OFFSET

0,1,1

STATUS

approved

editing

#2 by Russ Cox at Fri Mar 30 18:40:00 EDT 2012

AUTHOR

_Giovanni Teofilatto (g.teofilatto(AT)tiscalinet.it), _, Nov 29 2004

Discussion

Fri Mar 30

18:40

OEIS Server: https://oeis.org/edit/global/226

#1 by N. J. A. Sloane at Sun Feb 20 03:00:00 EST 2005

NAME

Largest prime p such that the sum of n consecutive primes plus p is equal to n^3.

DATA

5, 19, 41, 89, 163, 271, 631

OFFSET

0,1

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.

KEYWORD

nonn

AUTHOR

Giovanni Teofilatto (g.teofilatto(AT)tiscalinet.it), Nov 29 2004

STATUS

approved