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.
/* 5000 significant digits */ s=asin(1)*2; for(i=0,1000,s=s*ceil(1/s)-1; if(isprime(ceil(1/s))==1,print1(ceil(1/s),",")); );
From _Omar E. Pol_, Aug 20 2011 (Start): Illustration of initial terms as perimeters of squares (cf. Perry's comment above): . o o o o o o . o o o o o o o . o o o o o o o o . o o o o o o o o o . o o o o o o o o o o . o o o o o o o o o o o o o o o o o o o o o . . 1 4 8 12 16 20 (End)
a008574 0 = 1; a008574 n = 4 * n a008574_list = 1 : [4, 8 ..] -- Reinhard Zumkeller, Apr 16 2015
f[0] = 1; f[n_] := 4 n; Array[f, 59, 0] (* or *)
CoefficientList[ Series[(1 + x)^2/(1 - x)^2, {x, 0, 58}], x] (* Robert G. Wilson v, Jan 02 2011 *)
Join[{1},Range[4,232,4]] (* Harvey P. Dale, Aug 19 2011 *)
a[ n_] := 4 n + Boole[n == 0]; (* Michael Somos, Jan 07 2019 *)
{a(n) = 4*n + !n}; /* Michael Somos, Apr 16 2007 */
G.f. = 1 + x + 2*x^2 + 3*x^3 + 4*x^4 + 5*x^5 + 6*x^6 + 7*x^7 + 8*x^8 + 9*x^9 + ...
a028310 n = 0 ^ n + n a028310_list = 1 : [1..] -- Reinhard Zumkeller, Nov 06 2012
[n eq 0 select 1 else n: n in [0..75]]; // G. C. Greubel, Jan 05 2024
a:= n-> `if`(n=0, 1, n): seq(a(n), n=0..60);
Denominator@ CoefficientList[Series[Log[1+x], {x,0,75}], x] (* or *)
CoefficientList[ Series[(1 -x +x^2)/(1-x)^2, {x,0,75}], x] (* Robert G. Wilson v, Aug 14 2015 *)
Join[{1}, Range[75]] (* G. C. Greubel, Jan 05 2024 *)
LinearRecurrence[{2,-1},{1,1,2},80] (* Harvey P. Dale, Jan 29 2025 *)
{a(n) = (n==0) + max(n, 0)} /* Michael Somos, Feb 02 2004 */
A028310(n)=n+!n \\ M. F. Hasler, Jan 16 2012
def A028310(n): return n|bool(n)^1 # Chai Wah Wu, Jul 13 2023
[n + int(n==0) for n in range(76)] # G. C. Greubel, Jan 05 2024
G.f. = 1 + 3*x + 6*x^2 + 9*x^3 + 12*x^4 + 15*x^5 + 18*x^6 + 21*x^7 + 24*x^8 + ... From _Omar E. Pol_, Aug 20 2011: (Start) Illustration of initial terms as triangles: . o . o o o . o o o o o . o o o o o o o . o o o o o o o o o . o o o o o o o o o o o o o o o o o o o o o . . 1 3 6 9 12 15 (End)
a008486 0 = 1; a008486 n = 3 * n a008486_list = 1 : [3, 6 ..] -- Reinhard Zumkeller, Apr 17 2015
[0^n+3*n: n in [0..90] ]; // Vincenzo Librandi, Aug 21 2011
CoefficientList[Series[(1 + x + x^2) / (1 - x)^2, {x, 0, 80}], x] (* Vincenzo Librandi, Nov 23 2014 *)
a[ n_] := If[ n == 0, 1, 3 n]; (* Michael Somos, Apr 17 2015 *)
{a(n) = if( n==0, 1, 3 * n)}; /* Michael Somos, May 05 2015 */
For n=2, a(2)=14 because 14 is the most likely sum (of the possible sums 4, 5, ..., 24) to occur when tossing 2 pairs of six-sided dice. - _Dennis P. Walsh_, Jan 26 2012
a008589 = (* 7) a008589_list = [0, 7 ..] -- Reinhard Zumkeller, Jan 25 2013
[7*n : n in [0..50]]; // Wesley Ivan Hurt, Jun 06 2014
A008589:=n->7*n; seq(A008589(n), n=0..50); # Wesley Ivan Hurt, Jun 06 2014
Range[0, 1000, 7] (* Vladimir Joseph Stephan Orlovsky, May 27 2011 *) 7*Range[0,60] (* Harvey P. Dale, Feb 28 2023 *)
makelist(7*n,n,0,20); /* Martin Ettl, Dec 17 2012 */
a(n)=7*n \\ Charles R Greathouse IV, Jul 10 2016
From _Omar E. Pol_, Aug 20 2011: (Start) Illustration of initial terms: . o o o o o . o o o o o o . o o o o o o o . o o o o o o o o . o o o o o o o o o . o o o o o o o o . 1 o o o o o o o . 6 o o o o o o . 12 o o o o o . 18 . 24 (End) G.f. = 1 + 6*x + 12*x^2 + 18*x^3 + 24*x^4 + 30*x^5 + 36*x^6 + 42*x^7 + 48*x^8 + 54*x^9 + ...
[0^n+6*n: n in [0..60] ]; // Vincenzo Librandi, Aug 21 2011
1, seq(6*n, n=1..65);
Join[{1},6*Range[60]] (* Harvey P. Dale, Jul 21 2013 *)
a[ n_] := Boole[n == 0] + 6 n; (* Michael Somos, May 21 2015 *)
makelist(if n=0 then 1 else 6*n,n,0,65); /* Martin Ettl, Nov 12 2012 */
{a(n) = 6*n + (!n)};
[6*n+int(n==0) for n in range(66)] # G. C. Greubel, May 25 2023
a004277 n = 2 * n - 1 + signum (1 - n) a004277_list = 1 : [2, 4 ..] -- Reinhard Zumkeller, Dec 19 2013
[1] cat [2*n: n in [1..80]]; // Vincenzo Librandi, Jul 11 2015
Join[{1}, Table[2*n, {n, 200}]] (* Vladimir Joseph Stephan Orlovsky, Jul 10 2011 *)
Select[Range@ 105, PowerMod[#, #, # + 1] == 1 &] (* Robert G. Wilson v, Sep 26 2016 *)
G.f. = 1 + 5*x + 10*x^2 + 15*x^3 + 20*x^4 + 25*x^5 + 30*x^6 + 35*x^7 + ...
[0^n+5*n: n in [0..50] ]; // Vincenzo Librandi, Aug 21 2011
Join[{1}, LinearRecurrence[{2, -1}, {5, 10}, 100]] (* Jean-François Alcover, Dec 13 2018 *)
a(n)=0^n+5*n \\ Charles R Greathouse IV, Mar 19 2015
Digits := 200: P := proc(x) local y; y := ceil(evalf(1/x)); if isprime(y) then y else nextprime(y); fi; end; F := proc(x) local y,i,t1; y := x; t1 := []; for i from 1 to 50 do p := P(y); t1 := [op(t1),p]; y := p*y-1; od; t1; end; F(Pi-3);
$MaxExtraPrecision = 40; P[x_] := Module[{y}, y = Ceiling[1/x]; If[PrimeQ[y], y, NextPrime[y]]]; F[x_] := Module[{y, i, t1}, y = x; t1 = {}; For[i = 1, i <= 70, i++, AppendTo[t1, p = P[y]]; y = p*y-1]; t1]; F[Pi-3] (* Jean-François Alcover, Dec 16 2013, translated from Maple *)
0.705230171791800965147431682888248513743577639109154328192267913813919...
RealDigits[ Sum[1/Product[ Prime[i], {i, n}], {n, 58}], 10, 111][[1]] (* Robert G. Wilson v, Aug 05 2005 *)
RealDigits[Total[1/#&/@FoldList[Times,Prime[Range[100]]]],10,120][[1]] (* Harvey P. Dale, Aug 27 2019 *)
default(realprecision, 20080); p=1; s=x=0; for (k=1, 10^9, p*=prime(k); s+=1.0/p; if (s==x, break); x=s ); x*=10; for (n=0, 20000, d=floor(x); x=(x-d)*10; write("b064648.txt", n, " ", d)) \\ Harry J. Smith, Sep 21 2009
@CachedFunction
def pv(n):
a = 1
b = 0
for i in (1..n):
a *= nth_prime(i)
b += 1/a
return b
N(pv(100),digits=108) # From Maple code Jani Melik, Jul 22 2015
Comments