This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A065382 #18 May 22 2025 09:09:44
%S A065382 2,1,1,2,2,1,2,3,2,2,3,3,3,3,2,4,3,3,4,4,4,4,4,4,4,4,5,5,6,4,5,3,6,6,
%T A065382 7,5,5,6,4,8,5,6,6,8,6,8,5,7,5,11,4,6,9,7,8,9,8,7,7,9,7,8,7,12,5,9,9,
%U A065382 11,9,7,7,12,10,10,9,9,9,6,11,10,11,9,12,11,12,9,10,11,12,10,13,9,11,10
%N A065382 Number of primes between n(n+1)/2 (exclusive) and (n+1)(n+2)/2 (inclusive).
%C A065382 Inspired by the weaker Legendre conjecture that there should be at least one prime between n^2 and (n+1)^2.
%H A065382 T. D. Noe, <a href="/A065382/b065382.txt">Table of n, a(n) for n = 1..10000</a>
%e A065382 a(10) = 2 because between 10*(10+1)/2=55 and (10+1)*(10+2)/2=66 there are 2 primes: 59, 61.
%t A065382 Table[ PrimePi[n(n + 1)/2] - PrimePi[n(n - 1)/2], {n, 2, 96}]
%o A065382 (Python)
%o A065382 from sympy import primerange
%o A065382 def A065382(n): return sum(1 for p in primerange((n*(n+1)>>1)+1,((n+2)*(n+1)>>1)+1)) # _Chai Wah Wu_, May 22 2025
%Y A065382 A000217, A014085, A065383, A065384.
%Y A065382 Essentially the same as A066888 and A090970.
%K A065382 nonn
%O A065382 1,1
%A A065382 _Reinhard Zumkeller_, Nov 05 2001
%E A065382 Definition improved by _Robert G. Wilson v_, Apr 22 2003