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A158796 Index of first of three successive primes which sum to a cube. 3
85, 3696, 79700, 263166, 283353, 434935, 678277, 950264, 1043678, 1266169, 1321463, 1436753, 2629623, 3568796, 3604676, 3676738, 3713180, 5096401, 5558697, 7162624, 9303565, 9504536, 10988577, 12778681, 13108392, 18730119 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..1000

EXAMPLE

a(1)=85 because prime(85)+prime(86)+prime(87)=439+443+449=11^3=(A076306(1))^3

a(2)=3696 because prime(3696)+prime(3697)+prime(3698)=34603+34607+34613=47^3=(A076306(2))^3.

MAPLE

count:= 0:

for x from 3 while count < 30 do

  y:= x^3;

  r:= floor(y/3);

  p0:= prevprime(r); p1:= nextprime(p0); p2:= nextprime(p1);

  while p0 + p1 + p2 > y do

    p2:= p1;

    p1:= p0;

    p0:= prevprime(p0);

  od:

  while p0 + p1 + p2 < y do

    p0:= p1;

    p1:= p2;

    p2:= nextprime(p2);

  od:

  if p0 + p1 + p2 = y then

    count:= count+1;

    A[count]:= numtheory:-pi(p0);

  fi

od:

seq(A[i], i=1..count); # Robert Israel, Feb 10 2017

PROG

(Python)

from __future__ import division

from sympy import prevprime, nextprime, isprime, primepi

A158796_list, i = [], 3

while i < 10**6:

    n = i**3

    m = n//3

    pm, nm = prevprime(m), nextprime(m)

    k = n - pm - nm

    if isprime(m):

        if m == k:

            A158796_list.append(primepi(pm))

    else:

        if nextprime(nm) == k:

            A158796_list.append(primepi(pm))

        elif prevprime(pm) == k:

            A158796_list.append(primepi(pm)-1)

    i += 1 # Chai Wah Wu, Jun 01 2017

CROSSREFS

Cf. A076304, A076306.

Sequence in context: A017801 A201799 A017748 * A201796 A093285 A011813

Adjacent sequences:  A158793 A158794 A158795 * A158797 A158798 A158799

KEYWORD

nonn

AUTHOR

Zak Seidov, Nov 12 2009

STATUS

approved

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Last modified August 16 10:35 EDT 2017. Contains 290623 sequences.