A335739 - OEIS

A335739

Numbers k such that the area of an equilateral triangle of side k falls in between twin primes.

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 a 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