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A335739 Numbers k such that the area of an equilateral triangle of side k falls in between twin primes. 0
3, 4, 25, 98, 119, 123, 136, 267, 299, 318, 344, 423, 429, 443, 444, 522, 552, 571, 577, 588, 589, 639, 677, 739, 771, 817, 933, 993, 1115, 1212, 1393, 1503, 1558, 1580, 1629, 1756, 1799, 1852, 1871, 1884, 1991, 2027, 2063, 2197, 2345, 2380, 2583, 2585 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The number 3 is the only value where the area is between twin primes with 3 as one of the twins.

LINKS

Table of n, a(n) for n=1..48.

EXAMPLE

An equilateral triangle of side 3 has an area A = (sqrt(3)/4) * 3^2 = 3.89711, which is between 3 and 5, which are twin primes; so 3 is a term.

An equilateral triangle of side 17 has an area A = (sqrt(3)/4) * 17^2 = 125.14 which is between 125 and 127. These are not twin primes; so 17 is not term.

PROG

(PARI) isok(k) = my(A = floor(k^2*sqrt(3)/4)); if (! (A%2), A--); isprime(A) && isprime(A+2); \\ Michel Marcus, Dec 28 2020

CROSSREFS

Cf. A001359, A006512.

Sequence in context: A009391 A212696 A192346 * A055348 A004206 A302397

Adjacent sequences:  A335736 A335737 A335738 * A335740 A335741 A335742

KEYWORD

nonn

AUTHOR

Philip Mizzi, Dec 28 2020

STATUS

approved

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Last modified June 15 04:47 EDT 2021. Contains 345043 sequences. (Running on oeis4.)