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.
a(4)=8 because the 4th term of A031133 is the 8th prime number.
a(10)=8 because the 10th prime=29 is followed by primes 31 and 37, and 37 - 29 = 8.
a031131 n = a031131_list !! (n-1) a031131_list = zipWith (-) (drop 2 a000040_list) a000040_list -- Reinhard Zumkeller, Dec 19 2013
[NthPrime(n+2)-NthPrime(n): n in [1..100] ]; // Vincenzo Librandi, Apr 11 2011
P:= select(isprime, [2,seq(2*i+1,i=1..1000)]): P[3..-1] - P[1..-3]; # Robert Israel, Jan 25 2015
Differences[lst_]:=Drop[lst,2]-Drop[lst,-2]; Differences[Prime[Range[123]]] (* Vladimir Joseph Stephan Orlovsky, Aug 13 2009 *) Map[#3 - #1 & @@ # &, Partition[Prime@ Range[84], 3, 1]] (* Michael De Vlieger, Dec 17 2017 *)
ithprime(i+2)-ithprime(i) $ i = 1..65 // Zerinvary Lajos, Feb 26 2007
a(n)=my(p=prime(n));nextprime(nextprime(p+1)+1)-p \\ Charles R Greathouse IV, Jul 01 2013
BB = primes_first_n(67)
L = []
for i in range(65):
L.append(BB[2+i]-BB[i])
L
# Zerinvary Lajos, May 14 2007
The difference a(49) = 524 first occurs at prime(2158173265) - prime(2158173263) = 50949283633 - 50949283109 = 524. - _Jon E. Schoenfield_, Aug 29 2006
d = 0; lst = {}; {p, q, r} = {1, 2, 3}; Do[{p, q, r} = {q, r, Prime@n}; If[r - p > d, d = r - p; AppendTo[lst, {p, r}]; Print[{p, r-p, r}]], {n, 212550893}]; Last /@ lst - First /@ lst (* Robert G. Wilson v, May 17 2006 *)
dist = 0; n = 0; While[n<250000000, n++; tmp = Prime[n + 2] - Prime[n]; If[tmp > dist, dist = tmp; Print[tmp]];]; (* Sam Handler (sam_5_5_5_0(AT)yahoo.com), Aug 08 2006 *)
lst = {}; {p, q, r} = {1, 2, 3}; d = 0; Do[{p, q, r} = {q, r, Prime@n}; If[r - p > d, d = r - p; AppendTo[lst, {p, r}]; Print[{p, r-p, r}]], {n, 8050000}]; Last /@ lst (* Robert G. Wilson v, May 17 2006 *)
a(4)=10 because the 4th term of A031134 is the 10th prime number.
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