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A287686 Numbers that are sums of three consecutive primes (A034961) and also sums of squares of three consecutive primes (A133529). 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 19 22:36 EST 2020. Contains 332061 sequences. (Running on oeis4.)