A002942 -id:A002942 - cp's OEIS frontend

A271181 Read A002942 digit-by-digit, beginning with an initial 0.

0, 1, 4, 9, 6, 1, 5, 2, 6, 3, 9, 4, 4, 6, 1, 8, 1, 1, 2, 1, 4, 4, 1, 9, 6, 1, 6, 9, 1, 5, 2, 2, 6, 5, 2, 9, 8, 2, 4, 2, 3, 1, 6, 3, 4

Offset: 0

Yoga Nugraha, Apr 01 2016

Cf. A002942.

A102859 Numbers that when squared and written backwards give a square again.

Original entry on oeis.org

0, 1, 2, 3, 10, 11, 12, 13, 20, 21, 22, 26, 30, 31, 33, 99, 100, 101, 102, 103, 110, 111, 112, 113, 120, 121, 122, 130, 200, 201, 202, 210, 211, 212, 220, 221, 260, 264, 300, 301, 307, 310, 311, 330, 836, 990, 1000, 1001, 1002, 1003, 1010, 1011, 1012, 1013, 1020

Offset: 1

Sanita Kashcheyeva (sanits(AT)gmail.com), Mar 01 2005

Contains A002778. - Robert Israel, Sep 20 2015

Squares of these terms are in A061457. - Jon E. Schoenfield, May 17 2022

			a(7)=12 belongs to the sequence since writing 12^2 = 144 backwards gives 441 = 21^2.

Jon E. Schoenfield, Table of n, a(n) for n = 1..10000
Index entry for sequences related to reversing digits of squares

Cf. A002778, A002942.

Cf. A061457 (squares).

[n: n in [0..1100] | IsSquare(Seqint(Reverse(Intseq(n^2))))]; // Vincenzo Librandi, Sep 21 2015

rev:= proc(n)
  local L, Ln, i;
  L:= convert(n, base, 10);
  Ln:= nops(L);
  add(L[i]*10^(Ln-i), i=1..Ln);
end proc:
select(t -> issqr(rev(t^2)),[$0..10^5]); # Robert Israel, Sep 20 2015

Select[Range[1000], IntegerQ[Sqrt[FromDigits[Reverse[IntegerDigits[ #^2]]]]] &]

from itertools import count, islice
from sympy import integer_nthroot
def A102859_gen(startvalue=0): # generator of terms >= startvalue
    return filter(lambda n:integer_nthroot(int(str(n**2)[::-1]),2)[1], count(max(startvalue,0)))
A102859_list = list(islice(A102859_gen(),30)) # Chai Wah Wu, Nov 18 2022

a(n) = sqrt(A061457(n)). - Jon E. Schoenfield, May 17 2022

0 inserted by Jon E. Schoenfield, Sep 20 2015

A004165 Cubes written backwards.

Original entry on oeis.org

1, 8, 72, 46, 521, 612, 343, 215, 927, 1, 1331, 8271, 7912, 4472, 5733, 6904, 3194, 2385, 9586, 8, 1629, 84601, 76121, 42831, 52651, 67571, 38691, 25912, 98342, 72, 19792, 86723, 73953, 40393, 57824, 65664, 35605, 27845, 91395, 46, 12986, 88047, 70597, 48158

Offset: 1

N. J. A. Sloane

Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Vincenzo Librandi)

Cf. A000578 (cubes), A004086 (n written backwards).

Cf. A002942 (squares written backwards).

a:= n-> (s-> parse(cat(s[-i]$i=1..length(s))))(""||(n^3)):
seq(a(n), n=1..60);  # Alois P. Heinz, May 20 2022

Table[FromDigits[Reverse[IntegerDigits[n^3]]], {n, 1, 50}] (* Vincenzo Librandi, Aug 27 2013 *)
IntegerReverse[Range[50]^3] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 23 2019 *)

a(n) = fromdigits(Vecrev(digits(n^3))); \\ Michel Marcus, Jun 04 2019

def a(n): return int(str(n**3)[::-1])
print([a(n) for n in range(1, 45)]) # Michael S. Branicky, May 24 2022

a(n) = A004086(A000578(n)). - Michel Marcus, Jun 04 2019

More terms from Jeremy Gardiner, Sep 08 2002

A061226 a(n) = n^2 + (n^2 with digits reversed).

Original entry on oeis.org

0, 2, 8, 18, 77, 77, 99, 143, 110, 99, 101, 242, 585, 1130, 887, 747, 908, 1271, 747, 524, 404, 585, 968, 1454, 1251, 1151, 1352, 1656, 1271, 989, 909, 1130, 5225, 10890, 7667, 6446, 8217, 11000, 5885, 2772, 1661, 3542, 6435, 11330, 8327, 7227, 8228

Offset: 0

Amarnath Murthy, Apr 22 2001

			a(4) = 77 = 16 + 61; a(7) = 143 = 49 + 94.

Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Harry J. Smith)

Cf. A000290, A002942, A056964.

R:= n-> (s-> parse(cat(s[-i]$i=1..length(s))))(""||n):
a:= n-> (s-> s+R(s))(n^2):
seq(a(n), n=0..50);  # Alois P. Heinz, Sep 24 2018

nsr[n_]:=Module[{n2=n^2},n2+FromDigits[Reverse[IntegerDigits[n2]]]]; Array[ nsr,50,0] (* Harvey P. Dale, Jul 23 2012 *)

{a(n) = n^2+fromdigits(Vecrev(digits(n^2)))} \\ Seiichi Manyama, Sep 24 2018

a(n) = A000290(n) + A002942(n).

More terms from Patrick De Geest, May 29 2001

A002108 4th powers written backwards.

Original entry on oeis.org

1, 61, 18, 652, 526, 6921, 1042, 6904, 1656, 1, 14641, 63702, 16582, 61483, 52605, 63556, 12538, 679401, 123031, 61, 184491, 652432, 148972, 677133, 526093, 679654, 144135, 656416, 182707, 18, 125329, 6758401, 1295811, 6336331, 5260051, 6169761

Offset: 1

N. J. A. Sloane

T. D. Noe, Table of n, a(n) for n = 1..1000

Cf. A004086, A000583, A002942, A004165.

{This sequence} Intersection A000583 = A186080 (palindromes).

FromDigits[Reverse[IntegerDigits[#]]]&/@(Range[40]^4) (* Harvey P. Dale, May 03 2012 *)

a(n) = fromdigits(Vecrev(digits(n^4))); \\ Michel Marcus, Jun 04 2019

From Michel Marcus, Jun 04 2019: (Start)
a(n) = A004086(A000583(n)).
a(n) = A002942(n^2). (End)
a(n * 10^k) = a(n) for k >= 1. - Bernard Schott, Jun 04 2019

A074896 Squares written backwards and sorted, duplicates removed.

Original entry on oeis.org

1, 4, 9, 18, 46, 52, 61, 63, 94, 121, 144, 148, 163, 169, 423, 441, 484, 487, 522, 526, 652, 675, 676, 691, 925, 927, 961, 982, 1042, 1062, 1089, 1251, 1273, 1297, 1405, 1426, 1656, 1674, 1828, 1843, 1861, 4032, 4069, 4072, 4201, 4264, 4276, 4441, 4477

Offset: 1

Jason Earls, Sep 14 2002

			163 is in the sequence as it is 19^2 = 361 written backwards. - _David A. Corneth_, Aug 06 2022

David A. Corneth, Table of n, a(n) for n = 1..10000

Cf. A002942.

uptoqdigits(n) = {my(res = List()); forstep(i = 1, sqrtint(10^n), [1,1,1,1,1,1,1,1,2], listput(res, fromdigits(Vecrev(digits(i^2))))); Set(res)} \\ David A. Corneth, Aug 06 2022

A060998 Squares of 1 and primes, written backwards.

Original entry on oeis.org

1, 4, 9, 52, 94, 121, 961, 982, 163, 925, 148, 169, 9631, 1861, 9481, 9022, 9082, 1843, 1273, 9844, 1405, 9235, 1426, 9886, 1297, 9049, 10201, 90601, 94411, 18811, 96721, 92161, 16171, 96781, 12391, 10222, 10822, 94642, 96562, 98872, 92992, 14023

Offset: 1

Martin Goepfert (martin.goepfert(AT)fen-net.de), May 14 2001

Subsequence of A002942. - Michel Marcus, Nov 20 2015

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A001248, A002942, A008578.

revdigs := proc(n)
  local L, nL, j;
  L:= convert(n, base, 10);
  nL:= nops(L);
  add(L[i]*10^(nL-i), i=1..nL);
end:
map(t -> revdigs(t^2), [1,2,op(select(isprime, [seq(i,i=3..10^4,2)]))]); # Robert Israel, Nov 20 2015

Join[{1}, FromDigits[Reverse[IntegerDigits[#^2]]]&/@Prime[Range[100]]] (* Vincenzo Librandi, Nov 20 2015 *)

a(n) = if(n==1, 1, eval(concat(Vecrev(Str(prime(n-1)^2))))) \\ Altug Alkan, Nov 20 2015

More terms from Larry Reeves (larryr(AT)acm.org), May 15 2001

Offset changed from 0 to 1 by Altug Alkan, Nov 20 2015

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

A080334 n^2 read backwards, for n = 51, 50, 49, ...

Original entry on oeis.org

1062, 52, 1042, 4032, 9022, 6112, 5202, 6391, 9481, 4671, 1861, 61, 1251, 4441, 9631, 6921, 5221, 6511, 9801, 4201, 169, 9, 148, 487, 927, 676, 526, 675, 925, 484, 144, 4, 163, 423, 982, 652, 522, 691, 961, 441, 121, 1, 18, 46, 94, 63, 52, 61, 9, 4, 1

Offset: 51

N. J. A. Sloane, Mar 19 2003

This sequence breaks all the rules of the database, especially since the terms are in reverse order. It is included only because segments of it are sometimes given as puzzles.

Index entry for sequences related to reversing digits of squares

Cf. A002942 (which is the usual version of this sequence), A000290.

IntegerReverse/@(Range[51,1,-1]^2) (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 25 2019 *)

Write the squares backwards: 1, 4, 9, 61, 52, 63, 94, 46, 18, 1, 121, 441, 961, 691, ..., then reverse the sequence.

A129914 Irregular square reversible numbers. Numbers which when squared and written backwards give a square again, but don't satisfy reverse(n^2) = reverse(n)^2.

Original entry on oeis.org

26, 33, 99, 260, 264, 307, 330, 836, 990, 2285, 2600, 2636, 2640, 3070, 3168, 3300, 6501, 8360, 9900, 20508, 21468, 22850, 22865, 24846, 26000, 26360, 26400, 30693, 30700, 31680, 33000, 65010

Offset: 1

Robert J. Lemke Oliver (lemkeoliver(AT)gmail.com), Jun 05 2007

			33^2 = 1089 reversed is 9801 = 99^2.

Jon E. Schoenfield, Table of n, a(n) for n = 1..321 (all terms < 10^9).
Index entry for sequences related to reversing digits of squares

Cf. A102859, A002942.

cp's OEIS Frontend

A271181 Read A002942 digit-by-digit, beginning with an initial 0.

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A102859 Numbers that when squared and written backwards give a square again.

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A004165 Cubes written backwards.

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A061226 a(n) = n^2 + (n^2 with digits reversed).

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A002108 4th powers written backwards.

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A074896 Squares written backwards and sorted, duplicates removed.

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A060998 Squares of 1 and primes, written backwards.

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Maple

Mathematica

PARI

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

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