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.
nxt[{a_,b_}]:={b,Total[IntegerReverse[{a,b}]]};Flatten[Position[NestList[nxt,{0,1},4000][[All,1]],?PrimeQ]]-1 (* _Harvey P. Dale, Aug 24 2022 *)
a=0; b=1; for(n=2,3999, ispseudoprime(b=A004086(a)+A004086(a=b))&print1(n", ")) \\ M. F. Hasler, Jan 14 2011
a(14) = 0 + 1 + 1 + 2 + 3 + 5 + 8 + 13 + 39 + 124 + 514 + 836 + 1053 + 4139 + 12815 = 19553 is prime. a(31) = 0 + 1 + 1 + 2 + 3 + 5 + 8 + 13 + 39 + 124 + 514 + 836 + 1053 + 4139 + 12815 + 61135 + 104937 + 792517 + 1454698 + 9679838 + 17354310 + 9735140 + 1760750 + 986050 + 621360 + 113815 + 581437 + 1252496 + 7676706 + 13019288 + 94367798 + 178067380.
nxt[{a_,b_}]:={b,Total[FromDigits/@Reverse/@IntegerDigits[{a,b}]]};Accumulate[ Transpose[NestList[nxt,{0,1},40]][[1]]] (* Harvey P. Dale, Apr 04 2015 *)
with(transforms); f:=proc(n) option remember; if n <= 1 then n else digrev(f(n-1)+f(n-2)); fi; end; [seq(f(n),n=0..50)];
Clear[ BiF ]; BiF[ 0 ]=0; BiF[ 1 ]=1; BiF[ n_Integer ] := BiF[ n ]=Plus@@(IntegerDigits[ BiF[ n-2 ]+BiF[ n-1 ], 10 ]//(#*Array[ 10^#&, Length[ # ], 0 ])&); Array[ BiF, 40, 0 ]
nxt[{a_,b_}]:={b,FromDigits[Reverse[IntegerDigits[a+b]]]}; Transpose[ NestList[ nxt,{0,1},40]][[1]] (* Harvey P. Dale, Jun 15 2013 *)
from itertools import islice def A014258_gen(): # generator of terms a, b = 0, 1 yield 0 while True: yield b a, b = b, int(str(a+b)[::-1]) A014358_list = list(islice(A014258_gen(),20)) # Chai Wah Wu, Jan 15 2022
R:= n-> (s-> parse(cat(s[-i]$i=1..length(s))))(""||n):
a:= proc(n) option remember; `if`(n<2, n,
a(n-1) +R(a(n-2)))
end:
seq(a(n), n=0..50); # Alois P. Heinz, Jun 18 2014
Clear[ Bif ]; Bif[ 0 ]=0; Bif[ 1 ]=1; Bif[ n_Integer ] := Bif[ n ]=Bif[ n-1 ]+Plus@@(IntegerDigits[ Bif[ n-2 ], 10 ]//(#*Array[ 10^#&, Length[ # ], 0 ])&); Array[ Bif, 40, 0 ]
nxt[{a_,b_}]:={b,IntegerReverse[a]+b}; NestList[nxt,{0,1},40][[All,1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 04 2018 *)
lista(nn) = my(v=vector(nn)); v[2]=1; for(n=3, nn, v[n] = v[n-1] + fromdigits(Vecrev(digits(v[n-2])))); v \\ Jinyuan Wang, Aug 01 2021
a:=[0,0,1];[n le 3 select a[n] else Self(n-1) + Self(n-2) + Seqint(Reverse(Intseq(Self(n-3)))):n in [1..36]]; // Marius A. Burtea, Oct 23 2019
read("transforms") ;
A102111 := proc(n)
option remember;
if n <= 2 then
return op(n+1,[0,0,1]) ;
else
return procname(n-1)+procname(n-2)+digrev(procname(n-3)) ;
end if;
end proc:
seq(A102111(n),n=0..20) ; # R. J. Mathar, Nov 17 2012
R[n_]:=FromDigits[Reverse[IntegerDigits[n]]];Clear[a];a[0]=0;a[1]=0;a[2]=1;a [n_]:=a[n]=a[n-1]+a[n-2]+R[a[n-3]];Table[a[n], {n, 0, 40}]
nxt[{a_,b_,c_}]:={b,c,IntegerReverse[a]+b+c}; NestList[nxt,{0,0,1},40][[;;,1]] (* Harvey P. Dale, Jul 18 2023 *)
def R(n):
n_str = str(n)
reversedn_str = n_str[::-1]
reversedn = int(reversedn_str)
return reversedn
def A(n):
if n == 0:
return 0
elif n == 1:
return 0
elif n == 2:
return 1
elif n >= 3:
return A(n-1)+A(n-2)+R(A(n-3))
for i in range(0,20):
print(A(i)) # Dylan Delgado, Oct 23 2019
R:= n-> (s-> parse(cat(s[-i]$i=1..length(s))))(""||n):
a:= proc(n) option remember; `if`(n<3, binomial(n,2),
R(R(a(n-1)) + R(a(n-2)) + R(a(n-3))))
end:
seq(a(n), n=0..50); # Alois P. Heinz, Jun 18 2014
R[n_]:=FromDigits[Reverse[IntegerDigits[n]]];Clear[a];a[0]=0;a[1]=0;a[2]=1;a [n_]:=a[n]=R[R[a[n-1]]+R[a[n-2]]+R[a[n-3]]];Table[a[n], {n, 0, 40}]
rev[n_]:=FromDigits[Reverse[IntegerDigits[n]]]; nxt[{a_, b_, c_}] := {b, c, rev[rev[a] + rev[b] + rev[c]]}; Transpose[NestList[nxt,{0,0,1},40]][[1]] (* Harvey P. Dale, Mar 20 2015 *)
nxt[{a_,b_,c_}]:=With[{ir=IntegerReverse},{b,c,ir[ir[a]+ir[b]+ir[c]]}]; NestList[nxt,{0,0,1},40][[;;,1]] (* Harvey P. Dale, Jul 22 2025 *)
a(8)=12 because a(7)+a(6)=13+8=21 and the digits of 21 sorted in ascending order = 12. Also a(17)=4 because a(16)+a(15)=15+25=40 and the digits of 40 sorted in ascending order = 04, or just 4;
a:= proc(n) option remember; `if`(n<2, n, parse(cat(
sort(convert(a(n-1)+a(n-2), base, 10))[])))
end:
seq(a(n), n=0..77); # Alois P. Heinz, Aug 31 2022
a[0]:=0 a[1]:=1 a[n_] := a[n]=FromDigits[Sort[IntegerDigits[a[n-1]+a[n-2]]]] (* Peter J. C. Moses, Feb 08 2014 *) nxt[{a_,b_}]:={b,FromDigits[Sort[IntegerDigits[a+b]]]}; NestList[nxt,{0,1},70][[All,1]] (* Harvey P. Dale, Jul 27 2020 *)
a, terms = [0, 1], 66
[a.append(int("".join(sorted(str(a[-2]+a[-1]))))) for n in range(2, terms)]
print(a) # Michael S. Branicky, Aug 31 2022
R:= n-> (s-> parse(cat(s[-i]$i=1..length(s))))(""||n):
a:= proc(n) option remember; `if`(n<2, n,
R(a(n-1)) +a(n-2))
end:
seq(a(n), n=0..50); # Alois P. Heinz, Jun 18 2014
a[0] = 0; a[1] = 1; a[n_] := a[n] = FromDigits[ Reverse[ IntegerDigits[ a[n - 1]]]] + a[n - 2]; Table[ a[n], {n, 0, 36}] (* Robert G. Wilson v *)
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