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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
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
KEYWORD
nonn
AUTHOR
Zak Seidov, May 29 2017
STATUS
approved

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Last modified May 25 11:12 EDT 2024. Contains 372788 sequences. (Running on oeis4.)