A090785 Numbers that can be expressed as the difference of the squares of consecutive primes in just one way.

5, 16, 24, 48, 240, 288, 360, 432, 648, 672, 720, 840, 888, 960, 1080, 1128, 1248, 1320, 1392, 1488, 1560, 1608, 1680, 1728, 1800, 1920, 2040, 2088, 2112, 2232, 2280, 2400, 2520, 2568, 2640, 2808, 2832, 2880, 3120, 3240, 3312, 3360, 3432, 3672, 3912, 4080

Offset

1,1

Links

Table of n, a(n) for n=1..46.

Example

5 = 3^2 - 2^2.

Prog

(Python)
from sympy import primerange
from collections import Counter
def aupto(limit):
  sqps = [p*p for p in primerange(1, limit//2+1)]
  ways = Counter(sqps[i+1]-sqps[i] for i in range(len(sqps)-1))
  return sorted(k for k in ways if k <= limit and ways[k] == 1)
print(aupto(4080)) # Michael S. Branicky, May 16 2021

Crossrefs

Cf. A078667, A090781, A090783, A090784, A091878.

Sequence in context: A063232 A087747 A352754 * A069482 A274012 A102045

Adjacent sequences: A090782 A090783 A090784 * A090786 A090787 A090788

Keyword

nonn

Author

Ray G. Opao, Feb 08 2004

Extensions

More terms from Ray Chandler, Feb 11 2004

Status

approved