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

Author

Reinhard Zumkeller, Oct 22 2002

Keywords

• nonn

Crossrefs

Cf. A006094, A048761, A074927.

Programs

Mathematica

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

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

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.