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={0,2,1}; Print[2] For[n=3, n<=1000, n++, sum=Plus@@a; If[PrimeQ[sum], Print[sum]]; a=RotateLeft[a]; a[[3]]=sum]
a={0,2,1};Print[1];For[n=3,n<=1000,n++,sum=Plus@@a;If[PrimeQ[sum],Print[n]];a=RotateLeft[a]; a[[3]]=sum]
a[0]:=-1:a[1]:=2:a[2]:=2:for n from 3 to 42 do a[n]:=a[n-1]+a[n-2]+a[n-3] od: seq(a[n],n=0..42);
a[0] = -1; a[1] = a[2] = 2; a[n_] := a[n] = a[n - 1] + a[n - 2] + a[n - 3]; Table[ a[n], {n, 0, 35}] (* Robert G. Wilson v, Dec 09 2004 *)
LinearRecurrence[{1,1,1},{-1,2,2},34] (* Ray Chandler, Dec 08 2013 *)
Vec(-(1-3*x-x^2)/(1-x-x^2-x^3) + O(x^70)) \\ Michel Marcus, Sep 25 2015
a={3,1,1}; Print[0]; For[n=3, n<=1000, n++, sum=Plus@@a; If[PrimeQ[sum], Print[n]]; a=RotateLeft[a]; a[[3]]=sum]
a:=[1,1,0];; for n in [4..40] do a[n]:=a[n-1]+a[n-2]+a[n-3]; od; a; # G. C. Greubel, Apr 23 2019
R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1-2*x^2)/(1-x-x^2-x^3) )); // G. C. Greubel, Apr 23 2019
A081172 := proc(n) option remember; if n <= 2 then op(n+1,[1,1,0]) ; else add(procname(n-i),i=1..3) ; end if; end proc: # R. J. Mathar, Aug 09 2012
LinearRecurrence[{1,1,1}, {1,1,0}, 40] (* Vladimir Joseph Stephan Orlovsky, Jun 07 2011 *)
{ a1=1; a2=1; a3=0; write("b081172.txt",0," ",a1); write("b081172.txt",1," ",a2); write("b081172.txt",2," ",a3); for(n=3,500, a=a1+a2+a3; a1=a2; a2=a3; a3=a; write("b081172.txt",n," ",a) ) } \\ Harry J. Smith, Mar 20 2009
my(x='x+O('x^40)); Vec((1-2*x^2)/(1-x-x^2-x^3)) \\ G. C. Greubel, Apr 23 2019
((1-2*x^2)/(1-x-x^2-x^3)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Apr 23 2019
Northwest corner: 1 2 4 7 13 24 44 81 149 274 504 3 6 11 20 37 68 125 230 423 778 5 9 17 31 57 105 193 355 653 8 15 28 51 94 173 318 585 10 19 35 64 118 217 399 12 22 41 75 138 254 14 26 48 88 162 16 30 55 101 18 33 61 21 39 23
# maximum index in A73 such that A73 <= n.
A73floorIdx := proc(n)
local k ;
for k from 3 do
if A000073(k) = n then
return k ;
elif A000073(k) > n then
return k -1 ;
end if ;
end do:
end proc:
# tribonacci expansion coeffs of n
A278038 := proc(n)
local k,L,nres ;
k := A73floorIdx(n) ;
L := [1] ;
nres := n-A000073(k) ;
while k >= 4 do
k := k-1 ;
if nres >= A000073(k) then
L := [1,op(L)] ;
nres := nres-A000073(k) ;
else
L := [0,op(L)] ;
end if ;
end do:
return L ;
end proc:
A278038inv := proc(L)
add( A000073(i+2)*op(i,L),i=1..nops(L)) ;
end proc:
A135175 := proc(n,k)
option remember ;
local a,known,prev,nprev,kprev,freb ;
if n =1 then
A000073(k+2) ;
elif k>3 then
procname(n,k-1)+procname(n,k-2)+procname(n,k-3) ;
else
if k = 1 then
for a from 1 do
known := false ;
for nprev from 1 to n-1 do
for kprev from 1 do
if procname(nprev,kprev) > a then
break ;
elif procname(nprev,kprev) = a then
known := true ;
end if;
end do:
end do:
if not known then
return a ;
end if;
end do:
else
prev := procname(n,k-1) ;
freb := A278038(prev) ;
return A278038inv([0,op(freb)]) ;
end if;
end if;
end proc:
seq(seq(A135175(n,d-n),n=1..d-1),d=2..12) ; # R. J. Mathar, Jun 07 2022
a={1, 2, 2}; Print[2]; Print[2]; For[n=3, n<=1000, n++, sum=Plus@@a; If[PrimeQ[sum], Print[n]]; a=RotateLeft[a]; a[[3]]=sum]
Position[LinearRecurrence[{1,1,1},{1,2,2},75000],?PrimeQ]-1//Flatten (* _Harvey P. Dale, Sep 02 2016 *)
a={3,1,1}; Print[3]; For[n=3, n<=1000, n++, sum=Plus@@a; If[PrimeQ[sum], Print[sum]]; a=RotateLeft[a]; a[[3]]=sum]
a={1,1,1,1,1,1}; For[n=6, n<=1000, n++, sum=Plus@@a; If[PrimeQ[sum], Print[sum]]; a=RotateLeft[a]; a[[5]]=sum]
a={0,0,1,0}; For[n=4, n<=1000, n++, sum=Plus@@a; If[PrimeQ[sum], Print[n]]; a=RotateLeft[a]; a[[4]]=sum]
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