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A349708
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a(n) is the smallest positive number k such that (product of the first n odd primes) + k^2 is a square.
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1
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1, 1, 4, 1, 19, 53, 58, 97, 181, 4244, 2122, 31126, 16451, 297392, 2444006, 622249, 2909047, 216182072, 62801719, 769709491, 32522441312, 37859955467, 129549407177, 286721160343, 101419856449, 107709289064864, 72441253480727, 56099073382147, 5249126879235893
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OFFSET
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1,3
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COMMENTS
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LINKS
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EXAMPLE
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a(4)=1 because the product of the first 4 odd primes, 3*5*7*11 = 1155, is 34^2 - 1. a(5)=19 because 15015=3*5*7*11*13=124^2-19^2, and no positive integer less than 19 will work in this situation.
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PROG
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(PARI) a(n) = my(k=1, p=prod(k=2, n+1, prime(k))); while (!issquare(k^2+p), k++); k; \\ Michel Marcus, Jan 10 2022
(Python)
from math import isqrt
from sympy import primorial, divisors
m = primorial(n+1)//2
a = isqrt(m)
d = max(filter(lambda d: d <= a, divisors(m, generator=True)))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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a(15)-a(26) and corrections to a(9) and a(11) from Jinyuan Wang, Jan 07 2022
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STATUS
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approved
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