A287686 Numbers that are sums of three consecutive primes (A034961) and also sums of squares of three consecutive primes (A133529).

83, 366819, 1055019, 1947411, 2740107, 3694179, 6627579, 8851251, 9430899, 20243811, 28391619, 37545291, 38242083, 49459179, 56550291, 88205211, 101931891, 103429491, 108060339, 135085851, 176962659, 183973851, 194907051, 196911171, 212874531, 249687699, 271986651

Offset

1,1

Comments

The only prime number is 83.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Example

83=A034961(9)=A133529(2),
366819=A034961(11502)=A133529(69),
1055019=A034961(30105)=A133529(107),
1947411=A034961(52758)=A133529(139),
2740107=A034961(72260)=A133529(161),
3694179=A034961(95152)=A133529(185).

Prog

(Python)
from __future__ import division
from sympy import prevprime, nextprime, isprime
A287686_list, p2, q2, r2, r = [], 4, 9, 25, 5
while r < 10**6:
    n = p2+q2+r2
    m = n//3
    pm, nm = prevprime(m), nextprime(m)
    k = n - pm - nm
    if isprime(m):
        if m == k:
            A287686_list.append(n)
    else:
        if nextprime(nm) == k or prevprime(pm) == k:
            A287686_list.append(n)
    s = nextprime(r)
    p2, q2, r2, r = q2, r2, s**2, s # Chai Wah Wu, May 30 2017

Crossrefs

Cf. A034961 Sums of three consecutive primes. A133529 Sum of squares of three consecutive primes.

Sequence in context: A087189 A201727 A116263 * A087532 A116307 A093676

Adjacent sequences: A287683 A287684 A287685 * A287687 A287688 A287689

Keyword

nonn

Author

Zak Seidov, May 29 2017

Status

approved