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A373181
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k such that 0 = Sum_{j=1..k} A373223(k, j). The indices of the rows in Gauss's triangle with vanishing row sums.
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1
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1, 5, 9, 11, 15, 17, 19, 27, 31, 81, 83, 85, 91, 205, 207, 213, 2955, 50299, 50373, 50395, 50397, 50399, 50441, 50453, 50461, 50465, 50505, 50509, 50513, 50519, 50649, 50895, 50897, 50923, 50931, 50933, 50935, 50937, 51117, 51125, 51129, 51131, 51133, 51135, 51165
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OFFSET
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1,2
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COMMENTS
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Terms are odd.
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LINKS
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MAPLE
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select(n -> A373224(n) = 0, [seq(1..300)]);
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PROG
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(SageMath)
def is_a(n):
p = nth_prime(n)
r = (p - 1)//2
return 0 == sum((-1)^(r*((q - 1)//2)) for q in prime_range(p))
def aList(upto): return [n for n in range(1, upto, 2) if is_a(n)]
print(aList(222))
(PARI) KP(p, q) = kronecker(p, q);
isok(k) = my(vp=primes(k)); vecsum(vector(k, j, KP(vp[k], vp[j])*KP(vp[j], vp[k]))) == 0; \\ Michel Marcus, Jun 01 2024
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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