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

Author

Ray G. Opao, Feb 08 2004

Keywords

• nonn

Examples

			5 = 3^2 - 2^2.
		

Crossrefs

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

Programs

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

Extensions

More terms from Ray Chandler, Feb 11 2004