A014258 -id:A014258 - cp's OEIS frontend

A101764 Iccanobif semiprime indices: Indices of semiprime numbers in A014258.

8, 10, 13, 17, 23, 26, 28, 29, 31, 39, 42, 53, 55, 56, 73, 83, 94, 98, 101, 113, 114, 115, 121, 167, 217, 255, 266, 326, 327, 333, 367, 389, 397, 404, 409, 423, 425, 467, 497, 570, 631, 639, 749, 761

Offset: 1

Jonathan Vos Post and Ray Chandler, Dec 15 2004

This sequence also includes 815, 862, 943, 1013, 1106, 1204, 1319, 1398, 1419, 1554, 1669, 1729, 1762, 1801, 1847, 1874, 1930, 1977, and 2123. It might or might not include 791, 927, 1022, 1027, 1110, 1129, 1307, 1558, 1662, 1694, 1723, 1747, 1850, 1934, 1954, 1978, 2014, 2069, and 2077, but the required factoring proved rather difficult. There are no further terms below 2123. - Lucas A. Brown, Nov 12 2022

Lucas A. Brown, A101764.py.

Cf. A001358, A001129, A014258, A014259, A014260, A101763, A101765, A101766.

nxt[{a_,b_}]:={b,IntegerReverse[a+b]}; Flatten[Position[NestList[nxt,{0,1},500][[All,1]],?(PrimeOmega[#]==2&)]]-1 (* _Harvey P. Dale, Jun 05 2022 *)

Missing 367 inserted and new terms 570-761 added by Lucas A. Brown, Nov 12 2022

A101760 Iccanobif prime indices: indices of prime numbers in A014258.

Original entry on oeis.org

3, 4, 5, 7, 9, 18, 19, 21, 22, 25, 27, 47, 97, 107, 154, 186, 205, 303, 363, 1385, 1515, 1546, 2642, 2795, 2825, 3193

Offset: 1

Jonathan Vos Post and Ray Chandler, Dec 15 2004

No more terms through 10^4.

Cf. A000040, A001129, A014258-A014260, A101759-A101762.

A350779 Indices where Iccanobif numbers of the form A014258 decrease, i.e., numbers k such that A014258(k) < A014258(k-1).

Original entry on oeis.org

10, 17, 19, 20, 21, 23, 28, 31, 32, 39, 41, 45, 50, 55, 58, 60, 66, 70, 73, 75, 78, 83, 84, 90, 92, 95, 100, 101, 103, 105, 113, 114, 117, 123, 126, 129, 131, 140, 143, 147, 149, 151, 153, 155, 157, 163, 166, 167, 174, 176, 184, 197, 200, 206, 208, 210, 215, 217

Offset: 1

Chai Wah Wu, Jan 15 2022

			A014258(17) = 715297 < 739401 = A014258(16), so 17 is a term.

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Cf. A014258.

Flatten[Position[s,#]&/@Select[s=NestList[{Last@#,FromDigits@Reverse@IntegerDigits@Total@#}&,{0,1},220],!OrderedQ@#&]]  (* Giorgos Kalogeropoulos, Jan 16 2022 *)

from itertools import count, islice
def A350079_gen(): # generator of terms
    a, b = 0, 1
    for n in count(1):
        if b < a:
            yield n
        a, b = b, int(str(a+b)[::-1])
A350079_list = list(islice(A350079_gen(),20))

A001129 Iccanobif numbers: reverse digits of two previous terms and add.

Original entry on oeis.org

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, 173537220, 106496242, 265429972, 522619163

Offset: 0

N. J. A. Sloane

Alois P. Heinz, Table of n, a(n) for n = 0..1000 (terms 0..300 from T. D. Noe)

Cf. A001129, A014258, A014259, A014260.

a001129 n = a001129_list !! n
a001129_list = 0 : 1 : zipWith (+) iccanobifs (tail iccanobifs) where iccanobifs = map a004086 a001129_list
-- Reinhard Zumkeller, Jan 01 2012

a:=[0,1];[n le 2 select a[n] else Seqint(Reverse(Intseq(Self(n-1)))) + Seqint(Reverse(Intseq(Self(n-2)))):n in [1..35]]; // Marius A. Burtea, Oct 23 2019

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)) +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 ]=Plus@@Map[ Plus@@(#*Array[ 10^#&, Length[ # ], 0 ])&, Map[ IntegerDigits, {BIF[ n-1 ], BIF[ n-2 ]} ] ]; Array[ BIF, 40, 0 ]
nxt[{a_,b_}]:={b,Total[FromDigits/@Reverse/@IntegerDigits[ {a,b}]]}; Transpose[NestList[nxt,{0,1},40]][[1]] (* Harvey P. Dale, Jun 22 2011 *)
nxt[{a_,b_}]:={b,Total[IntegerReverse[{a,b}]]}; NestList[nxt,{0,1},40][[All,1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 07 2019 *)

A001129(n,a=0,b=1)={ n || return; while( n-->0, b=A004086(a)+A004086(a=b)); b }

A001129_list, r1, r2 = [0,1], 1, 0
for _ in range(10**2):
    l, r2 = r1+r2, r1
    r1 = int(str(l)[::-1])
    A001129_list.append(l) # Chai Wah Wu, Jan 03 2015

A014260 Iccanobif numbers: add a(n-1) to reversal of a(n-2).

Original entry on oeis.org

0, 1, 1, 2, 3, 5, 8, 13, 21, 52, 64, 89, 135, 233, 764, 1096, 1563, 8464, 12115, 16763, 67884, 104645, 153521, 699922, 825273, 1055269, 1427797, 11053298, 19030539, 108265550, 201768641, 257331442, 404198544, 648332296, 1094223700, 1786457546, 1859682447

Offset: 0

N. J. A. Sloane

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Cf. A000045, A001129, A014258, A014259.

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

A102111 Iccanobirt numbers (1 of 15): a(n) = 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, 13, 24, 44, 99, 185, 328, 612, 1521, 2956, 4693, 8900, 20185, 33049, 53332, 144483, 291848, 459666, 1135955, 2443813, 4246722, 12285846, 19716010, 34278280, 118852511, 154192582, 281332336, 550783729, 1117407516, 2301424427

Offset: 0

Jonathan Vos Post and Ray Chandler, Dec 30 2004

Digit reversal variation of tribonacci numbers A000073.

Inspired by Iccanobif numbers: A001129, A014258-A014260.

Cf. A102112-A102125, A102131, A102171.

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

A004086(a(n)) = A102119(n).

A102125 Iccanobirt numbers (15 of 15): a(n) = R(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, 42, 44, 18, 941, 472, 405, 729, 5071, 6313, 8675, 90601, 31591, 9853, 11733, 31865, 31149, 736481, 365533, 313416, 3154311, 9834802, 5123383, 7112507, 12796921, 35055832, 19867834, 56610708, 906334841, 561210372

Offset: 0

Jonathan Vos Post and Ray Chandler, Dec 30 2004

Digit reversal variation of tribonacci numbers A000073.

Inspired by Iccanobif numbers: A001129, A014258-A014260.

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Cf. A102111-A102124.

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(n) = A004086(A102117(n)).

A014259 Iccanobif numbers: add reversal of a(n-1) to a(n-2).

Original entry on oeis.org

0, 1, 1, 2, 3, 5, 8, 13, 39, 106, 640, 152, 891, 350, 944, 799, 1941, 2290, 2863, 5972, 5658, 14537, 79199, 113734, 516510, 129349, 1460431, 1469990, 2460072, 4170632, 4820786, 11040916, 66724797, 90783682, 95363506, 151320041, 235386657, 908003573, 610687466

Offset: 0

N. J. A. Sloane

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Cf. A000045, A001129, A014258, A014260.

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 *)

A004091 Fibonacci numbers written backwards.

Original entry on oeis.org

0, 1, 1, 2, 3, 5, 8, 31, 12, 43, 55, 98, 441, 332, 773, 16, 789, 7951, 4852, 1814, 5676, 64901, 11771, 75682, 86364, 52057, 393121, 814691, 118713, 922415, 40238, 9626431, 9038712, 8754253, 7882075, 5647229, 25303941, 71875142, 96188093, 68954236, 551433201, 141085561, 692419762, 734494334, 337804107, 713094311, 3091136381, 3705121792

Offset: 0

N. J. A. Sloane

Or, Fibonacci numbers reversed.

N. J. A. Sloane and Alois P. Heinz, Table of n, a(n) for n = 0..1000
N. J. A. Sloane, Transforms
N. J. A. Sloane, Maple program for A004091

Cf. A000045, A004170, A014258.

a004091 = a004086 . a000045  -- Reinhard Zumkeller, Mar 08 2013

[Seqint(Reverse(Intseq(Fibonacci(n)))): n in [0..50]]; // Vincenzo Librandi, Jan 17 2016

a:= n-> (s-> parse(cat(s[-i]$i=1..length(s))))(
         ""||((<<0|1>, <1|1>>^n)[1,2])):
seq(a(n), n=0..50);  # Alois P. Heinz, Apr 09 2015

FromDigits[Reverse[IntegerDigits[#]]]&/@Fibonacci[Range[50]] (* Harvey P. Dale, Jun 10 2011 *)
IntegerReverse[Fibonacci[Range[0,50]]] (* Harvey P. Dale, Jun 21 2024 *)

a(n) = fromdigits(Vecrev(digits(fibonacci(n)))); \\ Michel Marcus, Mar 25 2024

a(n) = A004086(A000045(n)). - Reinhard Zumkeller, Mar 08 2013

A102112 Iccanobirt numbers (2 of 15): a(n) = 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, 24, 62, 117, 167, 940, 1818, 2034, 11155, 17275, 74420, 142846, 162568, 885229, 1893336, 2978492, 10197702, 15039830, 38797423, 52888176, 100407789, 206394037, 1246986214, 2077887605, 6411178063, 12726051979

Offset: 0

Jonathan Vos Post and Ray Chandler, Dec 30 2004

Digit reversal variation of tribonacci numbers A000073.

Inspired by Iccanobif numbers: A001129, A014258-A014260.

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Cf. A102111-A102125.

R[n_]:=FromDigits[Reverse[IntegerDigits[n]]];Clear[a];a[0]=0;a[1]=0;a[2]=1;a [n_]:=a[n]=a[n-1]+R[a[n-2]]+a[n-3];Table[a[n], {n, 0, 40}]
nxt[{a_,b_,c_}]:={b,c,a+FromDigits[Reverse[IntegerDigits[b]]]+c}; Transpose[ NestList[nxt,{0,0,1},40]][[1]] (* Harvey P. Dale, Jul 29 2013 *)

A004086(a(n)) = A102120(n).

cp's OEIS Frontend

A101764 Iccanobif semiprime indices: Indices of semiprime numbers in A014258.

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A101760 Iccanobif prime indices: indices of prime numbers in A014258.

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A350779 Indices where Iccanobif numbers of the form A014258 decrease, i.e., numbers k such that A014258(k) < A014258(k-1).

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A001129 Iccanobif numbers: reverse digits of two previous terms and add.

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A014260 Iccanobif numbers: add a(n-1) to reversal of a(n-2).

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A102111 Iccanobirt numbers (1 of 15): a(n) = a(n-1) + a(n-2) + R(a(n-3)), where R is the digit reversal function A004086.

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A102125 Iccanobirt numbers (15 of 15): a(n) = R(R(a(n-1)) + R(a(n-2)) + R(a(n-3))), where R is the digit reversal function A004086.

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A014259 Iccanobif numbers: add reversal of a(n-1) to a(n-2).

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