A014258 -id:A014258 - cp's OEIS frontend

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.

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

Jonathan Vos Post and Ray Chandler, Dec 30 2004

Digit reversal variation of tribonacci numbers A000073.

Inspired by Iccanobif numbers: A001129, A014258-A014260.

Cf. A102111-A102125.

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}]

a(n) = A004086(A102115(n)).

A102118 Iccanobirt numbers (8 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, 31, 24, 26, 18, 86, 31, 531, 846, 8041, 8149, 63071, 16297, 71578, 649051, 629637, 6620531, 9129987, 55108361, 97885807, 551421261, 924514407, 5741283751, 9149127127, 58252941851, 92725334137, 511304721061

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, A102112, A102113, A102114, A102115, A102116, A102117, A102119, A102120, A102121, A102122, A102123, A102124, A102125.

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}]
Transpose[NestList[{#[[2]],#[[3]],FromDigits[Reverse[IntegerDigits[Total[ #]]]]}&,{0,0,1},40]][[1]] (* Harvey P. Dale, Dec 04 2012 *)

Incorrect formula removed by Georg Fischer, Dec 18 2020

A101759 Iccanobif prime indices: Indices of prime numbers in A001129.

Original entry on oeis.org

3, 4, 5, 7, 13, 39, 51, 65, 254, 315, 361, 423, 1109, 1497, 1701, 3711, 3814, 3847

Offset: 1

Jonathan Vos Post and Ray Chandler, Dec 15 2004

No more terms through 10^4.

Cf. A000040, A001129, A014258-A014260, A101760-A101762.

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

A101763 Iccanobif semiprime indices: Indices of semiprime numbers in A001129.

Original entry on oeis.org

8, 10, 15, 17, 35, 37, 47, 53, 62, 66, 74, 79, 110, 127, 146, 214, 231, 241, 242, 245, 250, 277, 293, 302, 343, 485, 525, 550, 599, 638, 687, 733, 805, 814

Offset: 1

Jonathan Vos Post and Ray Chandler, Dec 15 2004

This sequence also includes 881, 946, 954, 1086, 1753, and 1771. It might or might not include 838, 849, 1073, 1667, 1741, 1870, 2155, and 2478, but the required factoring proved rather difficult. There are no further terms below 2478. - Lucas A. Brown, Nov 19 2022

Lucas A. Brown, A101763.py.

Cf. A001358, A001129, A014258, A014259, A014260, A101764, A101765, A101766.

Missing 302 inserted and 525 added by Sean A. Irvine, Apr 29 2022

a(28)-a(34) from Lucas A. Brown, Nov 21 2022

A101765 Iccanobif semiprime indices: Indices of semiprime numbers in A014259.

Original entry on oeis.org

8, 9, 15, 16, 18, 22, 32, 37, 46, 53, 61, 62, 64, 79, 82, 106, 121, 129, 149, 153, 229, 241, 266, 301, 381, 411, 502

Offset: 1

Jonathan Vos Post and Ray Chandler, Dec 15 2004

This sequence also includes 742, 987, 1147, 1246, 1337, 1373, 1454, 1493, 1537, 1835, 1967, and 2265. It might or might not include 622, 630, 647, 817, 1247, 1402, 1422, 1477, 1649, 1781, 1818, 1867, 1874, and 2115, but the required factoring proved rather difficult. There are no further terms below 2265. - Lucas A. Brown, Nov 12 2022

Lucas A. Brown, A101765.py.

Cf. A001358, A001129, A014258, A014259, A014260, A101763, A101764, A101766.

a(27) from Lucas A. Brown, Nov 12 2022

A101766 Iccanobif semiprime indices: Indices of semiprime numbers in A014260.

Original entry on oeis.org

8, 16, 18, 21, 26, 38, 42, 44, 49, 54, 55, 57, 61, 67, 77, 78, 115, 123, 134, 145, 151, 154, 202, 218, 249, 286, 349, 403, 498, 539, 647

Offset: 1

Jonathan Vos Post and Ray Chandler, Dec 15 2004

This sequence also includes 790, 1161, 1347, 1418, 1595, 1761, and 2018. It might or might not include 769, 1394, 1795, 1983, 2093, 2178, but the required factoring proved rather difficult. There are no further terms below 2178. - Lucas A. Brown, Nov 12 2022

Lucas A. Brown, A101766.py.

Cf. A001358, A001129, A014258, A014259, A014260, A101763, A101764, A101765.

nxt[{a_,b_}]:={b,IntegerReverse[a]+b}; Flatten[Position[NestList[nxt,{0,1},600][[All,1]],?(PrimeOmega[#]==2&)]]-1 (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale, Jul 04 2018 *)

Offset changed to 1 by Jinyuan Wang, Aug 01 2021

a(31) from Lucas A. Brown, Nov 12 2022

A101762 Iccanobif prime indices: Indices of prime numbers in A014260.

Original entry on oeis.org

3, 4, 5, 7, 11, 13, 19, 22, 25, 30, 39, 71, 81, 98, 1041, 2942, 4377, 10410

Offset: 1

Jonathan Vos Post and Ray Chandler, Dec 15 2004

No more terms through 11000.

Cf. A000040, A001129, A014258, A014259, A014260, A101759, A101760, A101761.

Offset changed to 1 by Jinyuan Wang, Aug 02 2021

A072210 a(1)=a(2)=1; a(n)=reverse(reverse(a(n-1))+reverse(a(n-2))) for n > 2.

Original entry on oeis.org

1, 1, 2, 3, 5, 8, 31, 12, 43, 55, 98, 441, 332, 773, 16, 834, 994, 739, 6341, 3732, 9083, 2816, 1999, 37161, 46162, 73324, 10586, 838011, 933971, 771092, 615964, 396957, 9029221, 2098891, 1118123, 3107025, 4215248, 73123631, 16275022, 89398653, 95664775

Offset: 1

Joseph L. Pe, Jul 03 2002

I call this sequence the Fibonacci mirror sequence for the following reason. For n>2, the expression "a(n)=a(n-1)+a(n-2)" is a valid equation if read backwards. For example, "a(9)=a(8)+a(7)" is "43=12+31", which read backwards is 13+21=34, a valid equation.
Reverse(a(n))=reverse(a(n-1))+reverse(a(n-2)). a(n) is the least natural number k such that reverse(k)=reverse(a(n-1))+reverse(a(n-2)).
(Added Jul 06 2002) Actually, the previous comments are true only if reverse(a(n-1))+reverse(a(n-2)) does not end in the digit 0. It ends in 0 for n = 15, but for no other n < 3 * 10^4. Mark Lewis claims that n = 15 is the only such value of n. He observes that the first fifteen terms of a(n) are the reverses of the first fifteen terms of the Fibonacci sequence. The later terms of a(n) are the reverses of the terms of the Fibonacci sequence starting with 377, 61 (excluding these initial two terms). Lewis' argument depends on his assertion that the (377,61)-sequence is, modulo 10, periodic with period 12 and with no zeros-one for which he, as yet, offers only empirical evidence.

			a(9)=reverse(reverse(a(8))+reverse(a(7)))=reverse(21+13)=43.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
The Fibonacci Mirror Sequence

Cf. A001129, A014258.

rev[n_] := FromDigits[Reverse[IntegerDigits[n]]]; r = {1, 1}; For[i = 1, i < 30, i++, l = Length[r]; r = Append[r, rev[rev[r[[l]]] + rev[r[[l - 1]]]]]]; r
rev[n_]:=FromDigits[Reverse[IntegerDigits[n]]]; nxt[{a_,b_}]:={b,rev[ rev[ a]+ rev[b]]}; Transpose[NestList[nxt,{1,1},50]][[1]] (* Harvey P. Dale, Apr 25 2014 *)

More terms from Harvey P. Dale, Apr 25 2014

A101761 Iccanobif prime indices: Indices of prime numbers in A014259.

Original entry on oeis.org

3, 4, 5, 7, 21, 35, 97, 830, 947, 2627

Offset: 1

Jonathan Vos Post and Ray Chandler, Dec 15 2004

No more terms through 10^4.

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

A172524 Partial sums of Iccanobif numbers A001129.

Original entry on oeis.org

0, 1, 2, 4, 7, 12, 20, 33, 72, 196, 710, 1546, 2599, 6738, 19553, 80688, 185625, 978142, 2432840, 12112678, 29466988, 39202128, 40962878, 41948928, 42570288, 42684103, 43265540, 44518036, 52194742, 65214030, 159581828, 337649208

Offset: 0

Jonathan Vos Post, Feb 06 2010

The only primes in this sequence are: 2, 7 and 19553. The squares in this sequence begin: 0, 1, 4, 196.

			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.

Cf. A000040, A000045, A001129, A004086, A014258-A014260.

nxt[{a_,b_}]:={b,Total[FromDigits/@Reverse/@IntegerDigits[{a,b}]]};Accumulate[ Transpose[NestList[nxt,{0,1},40]][[1]]] (* Harvey P. Dale, Apr 04 2015 *)

a(n) = SUM[i=0..n] A001129(i) = SUM[i=0..n] {a(0) = 0, a(1) = 1, a(i+2) = R(a(i)) + R(a(i+1))} = SUM[i=0..n] A001129(i) = SUM[i=1..n] {a(0) = 0, a(1) = 1, a(i+2) = A004086(a(i)) + A004086(a(i+1))}.

cp's OEIS Frontend

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.

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A102118 Iccanobirt numbers (8 of 15): a(n) = R(a(n-1) + a(n-2) + a(n-3)), where R is the digit reversal function A004086.

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A101759 Iccanobif prime indices: Indices of prime numbers in A001129.

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A101763 Iccanobif semiprime indices: Indices of semiprime numbers in A001129.

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A101765 Iccanobif semiprime indices: Indices of semiprime numbers in A014259.

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A101766 Iccanobif semiprime indices: Indices of semiprime numbers in A014260.

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A101762 Iccanobif prime indices: Indices of prime numbers in A014260.

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A072210 a(1)=a(2)=1; a(n)=reverse(reverse(a(n-1))+reverse(a(n-2))) for n > 2.

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A101761 Iccanobif prime indices: Indices of prime numbers in A014259.

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A172524 Partial sums of Iccanobif numbers A001129.