A158796 Index of first of three successive primes which sum to a cube.

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

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