cp's OEIS Frontend

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.

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A102116 Iccanobirt numbers (6 of 15): a(n) = R(a(n-1)) + R(a(n-2)) + a(n-3), where R is the digit reversal function A004086.

Original entry on oeis.org

0, 0, 1, 1, 2, 4, 7, 13, 42, 62, 63, 104, 499, 1458, 9639, 18409, 101308, 903221, 943819, 1141966, 8512981, 9527388, 11871383, 55668051, 62931854, 72771964, 148399704, 517843422, 705114520, 398159926, 1173206822, 3621090124, 6895084900
Offset: 0

Views

Author

Jonathan Vos Post and Ray Chandler, Dec 30 2004

Keywords

Comments

Digit reversal variation of tribonacci numbers A000073.
Inspired by Iccanobif numbers: A001129, A014258-A014260.

Links

Crossrefs

Cf. A102111-A102125.

Programs

  • Mathematica
    R[n_]:=FromDigits[Reverse[IntegerDigits[n]]];Clear[a];a[0]=0;a[1]=0;a[2]=1;a [n_]:=a[n]=R[a[n-1]]+R[a[n-2]]+a[n-3];Table[a[n], {n, 0, 40}]
nxt[{a_,b_,c_}]:={b,c,FromDigits[Reverse[IntegerDigits[c]]]+ FromDigits[ Reverse[ IntegerDigits[b]]]+a}; Transpose[NestList[nxt,{0,0,1},40]][[1]] (* Harvey P. Dale, Oct 10 2014 *)

Formula

A004086(a(n)) = A102124(n).

A102117 Iccanobirt numbers (7 of 15): a(n) = R(a(n-1)) + R(a(n-2)) + R(a(n-3)), where R is the digit reversal function A004086.

Original entry on oeis.org

0, 0, 1, 1, 2, 4, 7, 13, 42, 62, 81, 68, 130, 135, 648, 1408, 9418, 17036, 79261, 87517, 150946, 736926, 1350266, 7899219, 16380155, 70858879, 162124155, 704415429, 1573821475, 7217219419, 15814925285, 73143352729, 160127403115
Offset: 0

Views

Author

Jonathan Vos Post and Ray Chandler, Dec 30 2004

Keywords

Comments

Digit reversal variation of tribonacci numbers A000073.
Inspired by Iccanobif numbers: A001129, A014258-A014260.

Links

Crossrefs

Cf. A102111-A102125.

Programs

  • Maple
    rev:= proc(n) local i, L;
L:= convert(n,base, 10);
add(L[-i]*10^(i-1),i=1..nops(L))
end proc:
A[0]:= 0: A[1]:= 0: A[2]:= 1:
RA[0]:=0: RA[1]:= 0: RA[2]:= 1:
for n from 3 to 100 do
  A[n]:= RA[n-1]+RA[n-2]+RA[n-3];
  RA[n]:= rev(A[n]);
od:
seq(A[n],n=0..100); # Robert Israel, Aug 04 2016
  • Mathematica
    R[n_]:=FromDigits[Reverse[IntegerDigits[n]]];Clear[a];a[0]=0;a[1]=0;a[2]=1;a [n_]:=a[n]=R[a[n-1]]+R[a[n-2]]+R[a[n-3]];Table[a[n], {n, 0, 40}]
nxt[{a_,b_,c_}]:={b,c,Total[IntegerReverse/@{a,b,c}]}; Transpose[ NestList[ nxt,{0,0,1},40]][[1]] (* The program uses the IntegerReverse function from Mathematica version 10 *) (* Harvey P. Dale, Nov 28 2015 *)

Formula

A004086(a(n)) = A102125(n).

A081434 Numbers such that RevBinary() = RevDecimal(), where RevDecimal(n) is the decimal reversal of n (A004086) and RevBinary(n) is the binary reversal of n (A030101).

Original entry on oeis.org

0, 1, 3, 5, 7, 9, 33, 92, 99, 313, 585, 717, 732, 759, 957, 5485, 5845, 7447, 9009, 15351, 32223, 39993, 53235, 53835, 71869, 73737, 77360, 96817, 319773, 377913, 585585, 1758571, 1934391, 1979791, 3129213, 5071705, 5259525, 5841485, 13162800
Offset: 1

Views

Author

Reinhard Zumkeller, Mar 20 2003

Keywords

Links

Crossrefs

Cf. A004086, A030101.
Cf. A007632, A081433, A007088.

Programs

  • Mathematica
    Select[Range[0, 100000], SameQ @@ IntegerReverse[#, {2, 10}] &] (* Amiram Eldar, Aug 05 2025 *)
  • PARI
    isok(k) = fromdigits(Vecrev(binary(k)), 2) == fromdigits(Vecrev(digits(k))); \\ Amiram Eldar, Aug 05 2025
  • Python
    def ok(n): return int(bin(n)[:1:-1], 2) == int(str(n)[::-1])
print([k for k in range(10**7) if ok(k)]) # Michael S. Branicky, Jan 30 2023

Formula

A030101(a(n)) = A004086(a(n)).

Extensions

More terms from Harry J. Smith, Dec 19 2007

A085329 Non-palindromic solutions to sigma(R(n)) = sigma(n), where R = A004086 is digit-reversal.

Original entry on oeis.org

528, 825, 1561, 1651, 4064, 4604, 5346, 5795, 5975, 6435, 15092, 15732, 21252, 23751, 25212, 29051, 34536, 38115, 39325, 39516, 51183, 52393, 53295, 53768, 59235, 61593, 63543, 64328, 69368, 70577, 77507, 81558, 82346, 85518, 86396
Offset: 1

Views

Author

Labos Elemer, Jul 04 2003

Keywords

Comments

Without the non-palindromic condition, the first 62 terms would be identical to the list of palindromes A002113. - M. F. Hasler, May 13 2025

Examples

			sigma(528) = sigma(825) = 1488.

Links

Crossrefs

Cf. A000203 (sigma), A004086 (R), A350867 (similar with d = sigma_0).

Programs

  • Mathematica
    nd[x_, y_] := 10*x+y tn[x_] := Fold[nd, 0, x] red[x_] := Reverse[IntegerDigits[x]] Do[s=DivisorSigma[1, n]; s1=DivisorSigma[1, tn[red[n]]]; If[Equal[s, s1]&&!Equal[n, tn[red[n]]], Print[{n, s}]], {n, 1, 1000000}]
srnQ[n_]:=Module[{idn=IntegerDigits[n],ridn},ridn=Reverse[idn];idn!=ridn && DivisorSigma[1,n]==DivisorSigma[1,FromDigits[ridn]]]; Select[Range[ 100000], srnQ] (* Harvey P. Dale, Oct 25 2011 *)
  • PARI
    select( {is_A085329(n, r=A004086(n))=sigma(n)==sigma(r)&&n!=r}, [1..50000]) \\ M. F. Hasler, May 13 2025
  • Python
    from sympy import divisor_sigma as sigma
def is_A085329(n): return sigma(n)==sigma(r:=int(str(n)[::-1])) and n!=r # M. F. Hasler, May 13 2025

Formula

Solutions to (A000203(x) = A000203(A004086(x)) and A004086(x) <> x).

A102114 Iccanobirt numbers (4 of 15): a(n) = R(a(n-1)) + a(n-2) + a(n-3), where R is the digit reversal function A004086.

Original entry on oeis.org

0, 0, 1, 1, 2, 4, 7, 13, 42, 44, 99, 185, 724, 711, 1026, 7636, 8104, 12680, 24361, 37126, 99214, 102786, 823541, 347328, 1750070, 1871440, 2539179, 13340862, 31214950, 21821254, 89768624, 95723002, 131622637, 921717757, 985062768
Offset: 0

Views

Author

Jonathan Vos Post and Ray Chandler, Dec 30 2004

Keywords

Comments

Digit reversal variation of tribonacci numbers A000073.
Inspired by Iccanobif numbers: A001129, A014258-A014260.

Crossrefs

Cf. A102111-A102125.

Programs

  • Mathematica
    R[n_]:=FromDigits[Reverse[IntegerDigits[n]]];Clear[a];a[0]=0;a[1]=0;a[2]=1;a [n_]:=a[n]=R[a[n-1]]+a[n-2]+a[n-3];Table[a[n], {n, 0, 40}]
nxt[{a_,b_,c_}]:={b,c,FromDigits[Reverse[IntegerDigits[c]]]+b+a}; Transpose[NestList[nxt,{0,0,1},40]][[1]]  (* Harvey P. Dale, May 30 2012 *)

Formula

A004086(a(n)) = A102122(n).

A102119 Iccanobirt numbers (9 of 15): a(n) = R(a(n-1) + a(n-2) + R(a(n-3))), where R is the digit reversal function A004086.

Original entry on oeis.org

0, 0, 1, 1, 2, 4, 7, 31, 24, 26, 36, 401, 994, 8541, 9369, 90481, 803101, 122309, 918349, 6691411, 1892158, 8837259, 38317811, 15086655, 45813926, 46917727, 407993841, 224348715, 25411507, 629951893, 2286023711, 6507846892, 9250302919
Offset: 0

Views

Author

Jonathan Vos Post and Ray Chandler, Dec 30 2004

Keywords

Comments

Digit reversal variation of tribonacci numbers A000073.
Inspired by Iccanobif numbers: A001129, A014258-A014260.

Crossrefs

Cf. A102111-A102125.

Programs

  • Mathematica
    R[n_]:=FromDigits[Reverse[IntegerDigits[n]]];Clear[a];a[0]=0;a[1]=0;a[2]=1;a [n_]:=a[n]=R[a[n-1]+a[n-2]+R[a[n-3]]];Table[a[n], {n, 0, 40}]

Formula

a(n) = A004086(A102111(n)).

A102120 Iccanobirt numbers (10 of 15): a(n) = R(a(n-1) + R(a(n-2)) + a(n-3)), where R is the digit reversal function A004086.

Original entry on oeis.org

0, 0, 1, 1, 2, 4, 7, 31, 24, 44, 711, 977, 8311, 1089, 4023, 53122, 51475, 33677, 412441, 945145, 6303211, 1027527, 8075903, 51363612, 74868455, 376085401, 68539284, 214889742, 927862936, 2360934421, 2982905123, 1968515515, 8282454457
Offset: 0

Views

Author

Jonathan Vos Post and Ray Chandler, Dec 30 2004

Keywords

Comments

Digit reversal variation of tribonacci numbers A000073.
Inspired by Iccanobif numbers: A001129, A014258-A014260.

Crossrefs

Cf. A102111-A102125.

Programs

  • Mathematica
    R[n_]:=FromDigits[Reverse[IntegerDigits[n]]];Clear[a];a[0]=0;a[1]=0;a[2]=1;a [n_]:=a[n]=R[a[n-1]+R[a[n-2]]+a[n-3]];Table[a[n], {n, 0, 40}]
nxt[{a_, b_, c_}] := {b, c, IntegerReverse[c + IntegerReverse[b] + a]}; NestList[nxt,{0,0,1},40][[All,1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 30 2017 *)

Formula

a(n) = A004086(A102112(n)).

A102121 Iccanobirt numbers (11 of 15): a(n) = R(a(n-1) + R(a(n-2)) + R(a(n-3))), where R is the digit reversal function A004086.

Original entry on oeis.org

0, 0, 1, 1, 2, 4, 7, 31, 24, 44, 99, 581, 427, 117, 6201, 6367, 4018, 8621, 16342, 41752, 18376, 15486, 185801, 336123, 551315, 925189, 7799571, 5524929, 5346628, 6800461, 15116342, 36822052, 98232826, 48616741, 398264631, 406948574
Offset: 0

Views

Author

Jonathan Vos Post and Ray Chandler, Dec 30 2004

Keywords

Comments

Digit reversal variation of tribonacci numbers A000073.
Inspired by Iccanobif numbers: A001129, A014258-A014260.

Crossrefs

Cf. A102111-A102125.

Programs

  • Mathematica
    R[n_]:=FromDigits[Reverse[IntegerDigits[n]]];Clear[a];a[0]=0;a[1]=0;a[2]=1;a [n_]:=a[n]=R[a[n-1]+R[a[n-2]]+R[a[n-3]]];Table[a[n], {n, 0, 40}]
nxt[{a_,b_,c_}]:={b,c,IntegerReverse[c+IntegerReverse[b]+IntegerReverse[a]]}; NestList[ nxt,{0,0,1},40][[;;,1]] (* Harvey P. Dale, Mar 23 2023 *)

Formula

a(n) = A004086(A102113(n)).

A102122 Iccanobirt numbers (12 of 15): a(n) = R(R(a(n-1)) + a(n-2) + a(n-3)), where R is the digit reversal function A004086.

Original entry on oeis.org

0, 0, 1, 1, 2, 4, 7, 31, 42, 26, 531, 302, 67, 909, 8721, 4522, 48811, 72152, 6487, 908821, 844702, 6572211, 9726782, 29139201, 58129562, 86185456, 139627251, 949140792, 656458225, 9962261161, 6171227123, 20114953831, 68392496992
Offset: 0

Views

Author

Jonathan Vos Post and Ray Chandler, Dec 30 2004

Keywords

Comments

Digit reversal variation of tribonacci numbers A000073.
Inspired by Iccanobif numbers: A001129, A014258-A014260.

Crossrefs

Cf. A102111-A102125.

Programs

  • Mathematica
    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]]+a[n-2]+a[n-3]];Table[a[n], {n, 0, 40}]
nxt[{a_,b_,c_}]:={b,c,IntegerReverse[IntegerReverse[c]+b+a]}; NestList[nxt,{0,0,1},40][[;;,1]] (* Harvey P. Dale, Sep 10 2024 *)

Formula

a(n) = A004086(A102114(n)).

A102123 Iccanobirt numbers (13 of 15): a(n) = R(R(a(n-1)) + a(n-2) + R(a(n-3))), where R is the digit reversal function A004086.

Original entry on oeis.org

0, 0, 1, 1, 2, 4, 7, 31, 42, 26, 711, 761, 49, 279, 8811, 1651, 44311, 38141, 55006, 45901, 34108, 990681, 161132, 5891031, 6129461, 8041777, 45820251, 74839842, 60558487, 202825861, 635089352, 309192535, 7549098331, 8252802091
Offset: 0

Views

Author

Jonathan Vos Post and Ray Chandler, Dec 30 2004

Keywords

Comments

Digit reversal variation of tribonacci numbers A000073.
Inspired by Iccanobif numbers: A001129, A014258-A014260.

Crossrefs

Cf. A102111-A102125.

Programs

  • Mathematica
    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]]+a[n-2]+R[a[n-3]]];Table[a[n], {n, 0, 40}]

Formula

a(n) = A004086(A102115(n)).
Previous Showing 11-20 of 587 results. Next

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