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