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 1-5 of 5 results.

A115763 Primes p such that the digits of p^2, reversed, include the digits of p as a substring.

Original entry on oeis.org

5, 87690769, 311314139, 44466725441, 38460053757197
Offset: 1

Views

Author

Giovanni Resta, Jan 30 2006

Keywords

Comments

a(6) > 6*10^14. - Giovanni Resta, Oct 21 2018

Examples

			311314139^2 = 969164(931413113)21.
		

Crossrefs

Extensions

a(5) from Giovanni Resta, Sep 11 2018

A115762 Numbers k such that the digits of k^3, reversed, include the digits of k as substring.

Original entry on oeis.org

1, 4, 5, 6, 9, 39, 67, 99, 670, 735, 999, 2424, 5619, 6700, 6966, 9999, 14597, 15458, 29266, 33795, 43259, 49664, 61256, 69566, 75463, 80238, 97155, 99999, 123798, 190544, 290105, 292660, 424068, 424846, 429163, 432590, 625503, 658458
Offset: 1

Views

Author

Giovanni Resta, Jan 30 2006

Keywords

Examples

			735^3 = 39706(537)5.
		

Crossrefs

Programs

  • Mathematica
    Select[Range[660000],SequenceCount[IntegerDigits[IntegerReverse[#^3]],IntegerDigits[#]]>0&] (* Harvey P. Dale, May 13 2025 *)

A115764 Primes p such that the digits of p^3, reversed, include the digits of p as a substring.

Original entry on oeis.org

5, 67, 695263, 994871, 5616469, 31471711, 43693817, 878757569, 5149409929, 7866434053, 8603497223, 13880125751
Offset: 1

Views

Author

Giovanni Resta, Jan 30 2006

Keywords

Examples

			31471711^3 = 3(11717413)21891966598431.
		

Crossrefs

A179803 Numbers that contain the digital reverse of their square root.

Original entry on oeis.org

1, 25, 36, 729, 5476, 927369, 32752729, 37724164, 42562576, 97357689, 2825135104, 4325166756, 4860041796, 123715399824, 167904077121, 247679410276, 389724269841, 442094669604, 486004179600, 610118772201, 7473372660009, 15049783154025, 23983713798489, 25315841305225
Offset: 1

Views

Author

Dominick Cancilla, Jul 27 2010

Keywords

Examples

			The square root of 729 is 27. 27's digital reverse is 72. 72 appears in 729.
		

Crossrefs

Cf. A115761.

Programs

  • Mathematica
    fQ[n_] := StringPosition[ IntegerString[n^2], StringReverse@ IntegerString@ n] != {}; k = 1; lst = {}; While[k < 3879404, If[ fQ@k, AppendTo[lst, k^2]]; k++ ]; lst (* Robert G. Wilson v, Jul 28 2010 *)
    drsrQ[n_]:=Module[{s=Sqrt[n]},MemberQ[Partition[Reverse[ IntegerDigits[ n]], IntegerLength[ s],1], IntegerDigits[s]]]; Select[Range[ 28*10^5]^2, drsrQ] (* Harvey P. Dale, Dec 15 2015 *)

Formula

a(n) = A115761(n)^2.

Extensions

More terms from Robert G. Wilson v, Jul 28 2010
Terms a(22) and beyond from Giovanni Resta, May 04 2020

A269588 Numbers n such that n^2 ends with the digits of n reversed (A004086(n)).

Original entry on oeis.org

1, 5, 6, 963, 9867, 65766, 69714, 6317056, 90899553, 169605719, 4270981082, 96528287587, 465454256742, 692153612536, 182921919071841, 655785969669834, 650700037578750084, 125631041500927357539, 673774165549097456624, 16719041449406813636569
Offset: 1

Views

Author

Keywords

Comments

a(29)>10^32 (if it exists)

Examples

			6317056^2 = 39905196507136 which ends with 6507136, so 6317056 is a term.
		

Crossrefs

Subsequence of A115761.

Programs

  • Mathematica
    Select[Range[10^7], Function[k, Take[IntegerDigits[#^2], -Length@ k] == Reverse@ k]@ IntegerDigits@ # &] (* Michael De Vlieger, Mar 04 2016 *)
  • PARI
    isA269588(n)=dn = digits(n); rn = subst(Polrev(dn), x, 10); nbd = #dn; (n^2 - rn) % 10^nbd == 0; \\ Michel Marcus, Mar 01 2016
    
  • PARI
    \\ printA269588len(d) prints all terms of the sequence with d digits
    rev(n) = eval(concat(Vecrev(Str(n))));
    { printA269588len(d) = my(l, u, n); l=ceil(d/2); u=floor(d/2); for(y=0, 10^l-1, n=rev(y^2 % 10^u)*10^l+y; if(#Str(n)==d && Mod(n, 10^d)^2==rev(n), print(n)); ); }
    \\ Max Alekseyev, Mar 07 2016

Extensions

a(18)-a(20) from Max Alekseyev, Mar 07 2016
a(21)-a(27) from Robert Gerbicz, Apr 03 2016
a(28) from Dieter Beckerle, Jun 09 2016
Showing 1-5 of 5 results.