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 A038822 #30 Nov 18 2024 07:39:11
%S A038822 25,21,16,16,17,14,16,14,15,14,16,12,15,11,17,12,15,12,12,13,14,10,15,
%T A038822 15,10,11,15,14,12,11,12,10,11,15,11,14,13,12,11,11,15,9,16,9,11,12,
%U A038822 12,12,8,15,12,11,10,10,13,13,12,10,16,7,12,11,13,15,8,11,10,12,12,13,9,10
%N A038822 Number of primes between 100n and 100n+99.
%C A038822 The number k first occurs in century A186311(k).
%D A038822 George P. Loweke, The Lore of Prime Numbers. New York: Vantage Press (1982): 91.
%H A038822 T. D. Noe, <a href="/A038822/b038822.txt">Table of n, a(n) for n = 0..9999</a>
%F A038822 a(n) = pi(100n+99) - pi(100n). - _Wesley Ivan Hurt_, Oct 03 2013
%e A038822 a(3) = 16 because there are 16 primes between 300 and 399 (namely, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397).
%e A038822 a(4) = 17 because there are 17 primes between 400 and 499 (401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499).
%p A038822 with(numtheory); A038822 := n->pi(100*n+99)-pi(100*n); seq(A038822(k), k=0..100); # _Wesley Ivan Hurt_, Oct 03 2013
%t A038822 Table[PrimePi[100n + 99] - PrimePi[100n], {n, 0, 71}]
%t A038822 Differences[PrimePi[100 Range[0,100]]] (* _Harvey P. Dale_, Feb 18 2021 *)
%o A038822 (PARI) a(n)=sum(i=100*n,100*n+99,isprime(i)) \\ _Charles R Greathouse IV_, Apr 28 2015
%o A038822 (PARI) a(n)= my(r=0, p=100*n, q=p+99); while((p=nextprime(p+1))<=q, r+=isprime(p)); r; \\ _Ruud H.G. van Tol_, Nov 17 2024
%Y A038822 Cf. A028505.
%Y A038822 Cf. A181098 (centuries without primes).
%Y A038822 Cf. A186393-A186408 (centuries having 1 to 16 primes), A186509 (17 primes).
%Y A038822 Cf. A094892, A098592.
%K A038822 nonn
%O A038822 0,1
%A A038822 _Jeff Burch_
%E A038822 Edited, corrected and extended by _Robert G. Wilson v_, Jan 29 2003