A004091 -id:A004091 - cp's OEIS frontend

A371508 Integers k such that A000045(k) + A004091(k) is prime (A000040).

1, 2, 81, 311, 6887, 9691, 296959

Offset: 1

Gonzalo Martínez, Mar 25 2024

			1 is a term since Fibonacci(1) = 1 plus its reversal is 1 + 1 = 2 which is prime (and for the same reason 2 is a term).
81 is a term since Fibonacci(81) = 37889062373143906 plus its reversal is 98823199699242779 which is prime.

Cf. A000040, A000045, A004091, A072366.

Select[Range[10^4], PrimeQ[(f = Fibonacci[#]) + IntegerReverse[f]] &] (* Amiram Eldar, Mar 25 2024 *)

a(7) from Michael S. Branicky, Jan 07 2025

A004170 Reversals of Fibonacci numbers (sorted).

Original entry on oeis.org

0, 1, 1, 2, 3, 5, 8, 12, 16, 31, 43, 55, 98, 332, 441, 773, 789, 1814, 4852, 5676, 7951, 11771, 40238, 52057, 64901, 75682, 86364, 118713, 393121, 814691, 922415, 5647229, 7882075, 8754253, 9038712, 9626431

Offset: 0

N. J. A. Sloane

The smallest Fibonacci number with 1, 2, 3,... trailing zeros is F(15), F(150), F(750), F(7500), F(75000),.... This provides an idea of how many digits may be "lost" by reversal. - R. J. Mathar, Mar 11 2013

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
Juan F. Pulido, José L. Ramírez, and Andrés R. Vindas-Meléndez, Generating Trees and Fibonacci Polyominoes, arXiv:2411.17812 [math.CO], 2024. See p. 8.

Cf. A000045, A004091.

Cf. A214855, A004086.

import Data.Set (fromList, deleteFindMin, insert)
a004170 n = a004170_list !! n
a004170_list = 0 : 1 : f (fromList us) vs where
   f s (x:xs) = m : f (insert x s') xs
     where (m,s') = deleteFindMin s
   (us,vs) = splitAt 120 $ drop 2 a004091_list
-- Reinhard Zumkeller, Mar 09 2013

Sort[FromDigits[Reverse[IntegerDigits[#]]]&/@Fibonacci[Range[0,40]]] (* Harvey P. Dale, Jun 17 2011 *)
IntegerReverse[Fibonacci[Range[0,40]]]//Sort (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 02 2019 *)

A133022 Product of n-th Fibonacci number and n-th Fibonacci number written backwards.

Original entry on oeis.org

0, 1, 1, 4, 9, 25, 64, 403, 252, 1462, 3025, 8722, 63504, 77356, 291421, 9760, 778743, 12697747, 12537568, 7584334, 38398140, 710406346, 208476181, 2168819074, 4004525952, 3905576425, 47722137553, 160019976838, 37728297243, 474332543035, 33479625520

Offset: 0

Omar E. Pol, Nov 07 2007

			403 = 13*31.

G. C. Greubel, Table of n, a(n) for n = 0..1000

Cf. A000045, A004091, A061205, A133019.

a:= n-> (f-> (s-> f*parse(cat(s[-i]$i=1..length(s))))(
          ""||f))(((<<0|1>, <1|1>>^n)[1, 2])):
seq(a(n), n=0..30);  # Alois P. Heinz, Apr 06 2018

#*FromDigits[Reverse[IntegerDigits[#]]]&/@Fibonacci[Range[0,40]] (* Harvey P. Dale, Oct 12 2012 *)

a(n) = A000045(n) * A004091(n).

Corrected and extended by Harvey P. Dale, Oct 12 2012

A062018 a(n) = n^n written backwards.

Original entry on oeis.org

1, 4, 72, 652, 5213, 65664, 345328, 61277761, 984024783, 1, 116076113582, 6528440016198, 352295601578203, 61085552860021111, 573958083098398734, 61615590737044764481, 771467633688162042728, 42457573569257080464393

Offset: 1

Amarnath Murthy, Jun 01 2001

			a(5) = 5213, as 5^5 = 3125.

Harry J. Smith, Table of n, a(n) for n = 1..200

Cf. A004086, A004093, A004156, A034906, A004094, A004167, A002108, A002118, A002138, A002140, A002232, A002239, A002241, A002942, A004165, A004087, A004091, A004096, A004098, A004150, A004153.

with(numtheory):for n from 1 to 50 do a := convert(n^n,base,10):b := add(10^(nops(a)- i)*a[i],i=1..nops(a)):printf(`%d,`,b); od:

Table[IntegerReverse[n^n],{n,20}] (* Harvey P. Dale, Jul 31 2022 *)

a(n) = { fromdigits(Vecrev(digits( n^n )))} \\ Harry J. Smith, Jul 29 2009

a(n) = A004086(n^n).

More terms from Jason Earls and Vladeta Jovovic, Jun 01 2001

A215649 Reversals of tribonacci numbers (sorted).

Original entry on oeis.org

0, 0, 1, 1, 2, 4, 7, 18, 31, 42, 44, 405, 472, 729, 941, 5071, 6313, 8675, 9853, 21066, 31591, 90601, 447014, 514121, 674557, 713322, 770074, 4606468, 7359831, 7575552, 8089735, 19520951, 52494292, 69005989, 106799181, 474396516, 777547433, 2586342311, 3016782802

Offset: 0

Jonathan Vos Post, Mar 09 2013

This is to A004170 as tribonacci numbers A000073 are to Fibonacci numbers A000045. Note that tribonacci(20) = 35890 is, upon reversal, 09853, then the leading 0 is truncated, making the 5-digit number into the 4-digit number 9853. Similarly, R(4700770) = 770074.

			A000073(n) for n = 7, 8, 9 = 13, 24, 44, 81. Reversed, those are 31, 42, 44, 18, and sorted that is 18, 31, 42, 44.

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

Cf. A000045, A000073, A004086, A004170, A004091, A140463, A214855, A004086.

Sort[FromDigits[Reverse[IntegerDigits[#]]]&/@LinearRecurrence[{1,1,1},{0,0,1,1},40]] (* Harvey P. Dale, Nov 22 2015 *)

A267551 Lucas numbers written backwards.

Original entry on oeis.org

2, 1, 3, 4, 7, 11, 81, 92, 74, 67, 321, 991, 223, 125, 348, 4631, 7022, 1753, 8775, 9439, 72151, 67442, 30693, 97046, 286301, 167761, 344172, 402934, 746017, 1589411, 8940681, 9430103, 7480784, 6911887, 34025721, 93233602, 28258333, 12581045, 30830478

Offset: 0

Vincenzo Librandi, Jan 17 2016

			81 is in the sequence because 7 + 11 = 18, which is 81 written backwards.

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Cf. A000032, A004086, A004091, A140463.

[Seqint(Reverse(Intseq(Lucas(n)))): n in [0..50]];

FromDigits[Reverse[IntegerDigits[#]]]&/@LucasL[Range[0, 50]]

a(n) = eval(concat(Vecrev(Str(fibonacci(n+1)+fibonacci(n-1))))); \\ Altug Alkan, Jan 17 2016

a(n) = A004086(A000032(n)).

A382082 F(k) such that F(k) + (F(k) reversed) is a palindrome, where F(k) is a Fibonacci number.

Original entry on oeis.org

0, 1, 2, 3, 13, 21, 34, 144, 233, 610, 4181, 832040, 102334155, 1134903170, 20365011074, 12200160415121876738

Offset: 1

Vincenzo Librandi, Mar 21 2025

Conjecture: The sequence appears to be finite.

The next term, F(k), has k > 3*10^5, if it exists. - Amiram Eldar, Mar 21 2025

			144 is in the sequence because 144 + 441 = 585 is a palindrome.

Intersection of A000045 and A015976.

Cf. A002113, A004086, A004091, A352124.

Rev := func;
[0] cat  [Fibonacci(n): n in [2..2*10^4] | q eq Rev(q) where q is Fibonacci(n)+Rev(Fibonacci(n))];

Mathematica

DeleteDuplicates@ Select[Fibonacci[Range[0, 100]], PalindromeQ[# + IntegerReverse[#]] &] (* Amiram Eldar, Mar 21 2025 *)

cp's OEIS Frontend

A371508 Integers k such that A000045(k) + A004091(k) is prime (A000040).

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A004170 Reversals of Fibonacci numbers (sorted).

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A133022 Product of n-th Fibonacci number and n-th Fibonacci number written backwards.

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Maple

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A062018 a(n) = n^n written backwards.

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Maple

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A215649 Reversals of tribonacci numbers (sorted).

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Mathematica

A267551 Lucas numbers written backwards.

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Magma

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A382082 F(k) such that F(k) + (F(k) reversed) is a palindrome, where F(k) is a Fibonacci number.

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