A352605 Primes p such that the floor of the area of a triangle with sides p-1, p and p+1 is prime.

3, 41, 97, 127, 163, 179, 239, 277, 367, 439, 443, 541, 569, 571, 577, 593, 677, 719, 809, 877, 1013, 1087, 1201, 1259, 1439, 1553, 1601, 1609, 1721, 1871, 1879, 1889, 2063, 2143, 2179, 2273, 2281, 2689, 2803, 2819, 2887, 3137, 3313, 3511, 3527, 3637, 3797, 3847, 3911, 4049, 4091, 4441, 4933

Offset

1,1

Comments

Primes p such that floor(p*sqrt(3*(p^2-4))/4) is prime.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(3) = 97 is a term because 97 is prime, the area of a triangle with sides 96, 97 and 98 is 4073.35..., and 4073 is prime.

Maple

filter:= p -> isprime(floor(p/4*sqrt(3*(p^2-4)))):
select(filter, [seq(ithprime(i), i=1..10000)]);

Crossrefs

Cf. A096378.

Sequence in context: A100765 A372222 A092168 * A360930 A229080 A289270

Adjacent sequences: A352602 A352603 A352604 * A352606 A352607 A352608

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Mar 22 2022

Status

approved