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.

Showing 1-6 of 6 results.

A061231 n - the reversal of n is a nonzero square.

Original entry on oeis.org

10, 21, 32, 40, 43, 51, 54, 62, 65, 73, 76, 84, 87, 90, 95, 98, 1030, 1100, 1140, 1210, 1250, 1320, 1360, 1430, 1470, 1540, 1580, 1650, 1690, 1760, 1870, 1980, 2031, 2101, 2141, 2211, 2251, 2321, 2361, 2431, 2471, 2541, 2581, 2651, 2691, 2761, 2871, 2981
Offset: 0

Views

Author

Amarnath Murthy, Apr 23 2001

Keywords

Examples

			a(4) = 40 as 40 - 4 = 36 = 6^2; a(9)= 65 as 65- 56 = 9 = 3^2.

Links

Crossrefs

Cf. A061230.

Programs

  • Mathematica
    nzsQ[n_]:=Module[{c=n-IntegerReverse[n]},c!=0&&IntegerQ[Sqrt[c]]]; Select[ Range[3000],nzsQ] (* The program uses the IntegerReverse function from Mathematica version 10 *) (* Harvey P. Dale, Jun 05 2016 *)

Extensions

More terms from Patrick De Geest, May 28 2001

A245361 Numbers n such that (reversal of digits of n) + 1 is a square (ignoring leading zeros).

Original entry on oeis.org

3, 8, 30, 36, 42, 51, 53, 80, 84, 99, 300, 323, 341, 360, 384, 387, 420, 422, 426, 510, 530, 552, 575, 576, 591, 800, 825, 827, 840, 861, 882, 990, 993, 998, 3000, 3032, 3069, 3072, 3201, 3230, 3264, 3276, 3410, 3441, 3477, 3483, 3600, 3633, 3648, 3671, 3806
Offset: 1

Views

Author

K. D. Bajpai, Jul 18 2014

Keywords

Comments

(Reversal of digits of prime p) plus 1 is square is given in A167217.

Examples

			84 is in the sequence because reversal of its digits is 48 and 48 + 1 = 49 = 7^2.
510 is in the sequence because reversal of its digits is 15 and 15 + 1 = 16 = 4^2.

Links

Crossrefs

Cf. A000290, A061230, A061457, A167217.

Programs

  • Mathematica
    Select[Range[10^4],IntegerQ[Sqrt[FromDigits[Reverse[IntegerDigits[#]]] + 1]] &]
  • PARI
    revint(n) = eval(concat(Vecrev(Str(n))))
select(n->issquare(revint(n)+1), vector(4000, n, n)) \\ Colin Barker, Jul 20 2014

A356648 Numbers whose square is of the form k + reversal of digits of k, for some k.

Original entry on oeis.org

2, 4, 11, 22, 25, 33, 101, 121, 141, 202, 222, 264, 303, 307, 451, 836, 1001, 1111, 1221, 1232, 2002, 2068, 2112, 2222, 2305, 2515, 2626, 2636, 2776, 3003, 3958, 3972, 4015, 4081, 7975, 8184, 9757, 10001, 10201, 10401, 11011, 11121, 11211, 12012, 12021, 12221, 13046, 16581, 20002
Offset: 1

Views

Author

Nicolay Avilov, data a(10)-a(37) from Oleg Sorokin, Dec 10 2022

Keywords

Comments

Square roots of the squares in A067030.

Examples

			4 is a term since 4^2 = 16 = 8 + 8;
11 is a term since 11^2 = 121 = 29 + 92 is sum of k=29 and its reversal 92;
22 is a term since 22^2 = 484 = 143 + 341;
10201 is a term since 10201^2 = 104060401 = 100030400 + 4030001.

Links

Crossrefs

Cf. A056964, A061230, A067030, A358880, A358984.

Programs

  • PARI
    L=vectorsmall(100000);
\\ Takes a few minutes of CPU time
for (k=1, 2*10^8, my(d=digits(k), r=fromdigits(Vecrev(d)), s); if (issquare(k+r, &s), L[s]=1));
for (k=1, 21000, if(L[k], print1(k,", "))) \\ Hugo Pfoertner, Dec 13 2022
(C++, Haskell) See Code Golf link.

Formula

a(n) = sqrt(A358880(n)). - Michel Marcus, Dec 25 2022

Extensions

a(38) and beyond from Hugo Pfoertner, Dec 12 2022

A358984 The number of n-digit numbers k such that k + digit reversal of k (A056964) is a square.

Original entry on oeis.org

3, 8, 19, 0, 169, 896, 1496, 3334, 21789, 79403, 239439, 651236, 1670022, 3015650, 27292097, 55608749, 234846164, 366081231, 2594727780, 6395506991
Offset: 1

Views

Author

Nicolay Avilov, Dec 08 2022

Keywords

Comments

Number of terms of A061230 which are n digits long.

Examples

			a(1) = 3 because there are 3 single-digit numbers: 0, 2, 8 such that b + b = m^2, for example, 8 + 8 = 16 = 4^2;
a(2) = 8 because there are 8 two-digit numbers: 29, 38, 47, 56, 65, 74, 83, 92 such that bc + cb = m^2, for example, 29 + 92 = 121 = 11^2.

Links

Crossrefs

Cf. A056964, A061230, A356648.

Programs

  • Mathematica
    a[n_]:=Length[Select[Table[k, {k, 10^(n-1),10^n-1}],IntegerQ[Sqrt[#+FromDigits[Reverse[IntegerDigits[#]]]]]&]]; Array[a,10] (* Stefano Spezia, Dec 09 2022 *)
  • Python
    from math import isqrt
def s(n): return isqrt(n)**2 == n
def c(n): return s(n + int(str(n)[::-1]))
def a(n): return 3 if n == 1 else sum(1 for k in range(10**(n-1), 10**n) if c(k))
print([a(n) for n in range(1, 7)]) # Michael S. Branicky, Dec 08 2022

Extensions

a(9)-a(10) from Michael S. Branicky, Dec 08 2022
a(11)-a(20) from Talmon Silver, Dec 25 2022

A359011 Numbers k such that k^2 + the reversal of k^2 is a square.

Original entry on oeis.org

0, 231, 9426681, 8803095102, 56017891104, 4811618419542
Offset: 1

Views

Author

Michel Marcus, Dec 11 2022

Keywords

Crossrefs

Cf. A056964, A061230.

Extensions

a(1)-a(5) from Douglas McNeil and Zak Seidov, Nov 09 2010
a(6) from Giovanni Resta, Sep 26 2011

A289140 Positive numbers k such that rev(k)^2 + rev(k^2) is a square, where rev(n) = A004086(n) is the digital reverse of n.

Original entry on oeis.org

998586, 3632658, 9985860, 36326580, 74471091, 99664458, 99858600, 363265800, 634826115, 743193501, 744710910, 756335085, 759317343, 996644580, 998586000, 3632658000, 6348261150, 7177621788, 7431935010, 7447109100, 7563350850, 7593173430, 9966445800
Offset: 1

Views

Author

Giovanni Resta, Jun 26 2017

Keywords

Comments

Every term must be a multiple of 3.

Examples

			998586 is a term since rev(998586^2) + 685899^2 = 1079100^2.

Crossrefs

Cf. A004086, A061230, A061231, A068536, A102859, A113798, A202386, A256515.

Programs

  • Mathematica
    rev[n_] := FromDigits@ Reverse@ IntegerDigits@ n; Parallelize@ Select[3 Range[4 10^6], IntegerQ@ Sqrt[rev[#^2] + rev[#]^2] &]
  • PARI
    isok(n) = issquare(fromdigits(Vecrev(digits(n)))^2 + fromdigits(Vecrev(digits(n^2)))); \\ Michel Marcus, Jun 29 2017
Showing 1-6 of 6 results.

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