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A076621 Least square greater than the product of two successive primes. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
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
Sequence in context: A348233 A110833 A225808 * A134937 A076431 A221856
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Oct 22 2002
STATUS
approved

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Last modified May 19 00:35 EDT 2024. Contains 372666 sequences. (Running on oeis4.)