A076621 Least square greater than the product of two successive primes.

9, 16, 36, 81, 144, 225, 324, 441, 676, 900, 1156, 1521, 1764, 2025, 2500, 3136, 3600, 4096, 4761, 5184, 5776, 6561, 7396, 8649, 9801, 10404, 11025, 11664, 12321, 14400, 16641, 17956, 19044, 20736, 22500, 23716, 25600, 27225, 28900, 30976, 32400, 34596, 36864

Offset

1,1

Links

Table of n, a(n) for n=1..43.

Formula

a(n) = A048761(A006094(n)).

a(n) = prime(n)*prime(n+1)+((prime(n)-(prime(n+1))/2)^2 = A006094(n) + A074927(n) for n > 1.

a(n) = ((prime(n)+prime(n+1))/2)^2 for n > 1.

Mathematica

Ceiling[Sqrt[Times@@#]]^2&/@Partition[Prime[Range[50]], 2, 1] (* Harvey P. Dale, Aug 26 2013 *)

Prog

(Python)
from sympy import prime, primerange
def aupton(terms):
    primes = list(primerange(3, prime(terms+1)+1))
    return [9] + [((p+q)//2)**2 for p, q in zip(primes[:-1], primes[1:])]
print(aupton(43)) # Michael S. Branicky, Sep 16 2021

Crossrefs

Cf. A006094, A048761, A074927.

Sequence in context: A348233 A110833 A225808 * A134937 A076431 A221856

Adjacent sequences: A076618 A076619 A076620 * A076622 A076623 A076624

Keyword

nonn

Author

Reinhard Zumkeller, Oct 22 2002

Status

approved