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 1-8 of 8 results.

A030175 When squared gives number composed of digits {1,2,3}.

Original entry on oeis.org

1, 11, 111, 36361, 363639, 461761, 3636361, 34815389, 362397739, 176412364139, 57637950363639, 3497458093147239, 56843832676142723489, 557963558954625926861
Offset: 1

Views

Author

Patrick De Geest

Keywords

Links

Crossrefs

Cf. A030174; A000290.
Cf. A006716 = A027675^2, A030176 = A030177^2, A058411^2 = A058412, ..., A058473^2 = A058474.
Cf. A136808, A136809, ..., A137147: n and n^2 have digits {...}.
Cf. A277959^2 = A277946 and A277960^2 = A277947: squares whose largest digit is 2 resp. 3.

Programs

  • Mathematica
    Do[ If[ Union[ Join[{1, 2, 3}, IntegerDigits[n^2] ] ] == {1, 2, 3}, Print[n] ], {n, 0, 10^9}]
  • PARI
    lista(nn) = for(n=1, nn, if(setminus(vecsort(digits(n^2), , 8), [1, 2, 3])==[], print1(n, ", "))) \\ Iain Fox, Nov 16 2017

Formula

a(n)^2 = A030174(n). - M. F. Hasler, Nov 16 2017

Extensions

More terms from Patrick De Geest, Mar 01 2000
More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 14 2005
Offset corrected by Iain Fox, Nov 16 2017

A122986 Squares mod 1000.

Original entry on oeis.org

0, 1, 4, 9, 16, 24, 25, 36, 41, 44, 49, 56, 64, 76, 81, 84, 89, 96, 100, 104, 116, 121, 124, 129, 136, 144, 156, 161, 164, 169, 176, 184, 196, 201, 204, 209, 216, 224, 225, 236, 241, 244, 249, 256, 264, 276, 281, 284, 289, 296, 304, 316, 321, 324, 329, 336, 344
Offset: 1

Views

Author

Sergio Pimentel, Sep 22 2006

Keywords

Comments

Possible last three digits of n^2 (leading zeros omitted).
Range of A174452; A010461 is a subset; and also all squares less than 1000 belong to this sequence; the sequence is finite with A000993(3)=159 terms: a(159)=996 is the last term.

Examples

			The last three digits of n^2 can be 000, 001, 236, 241, 996, etc. but not 002, 003, 237, 238, etc.

Links

Crossrefs

Cf. A036688, A010382, A010411, A010462, A010421, A174452.
Cf. A006716, A053975, A027676, A027678, A122987, A122988.
Row 1000 of A096008.

Programs

  • Magma
    [n: n in [0..999] | IsSquare(R! n) where R:= ResidueClassRing(1000)]; // Vincenzo Librandi, Dec 29 2019
  • Maple
    s:={}: for n from 0 to 999 do s:=s union {n^2 mod 1000}: od: op(s); # Nathaniel Johnston, Jun 22 2011
  • Mathematica
    Union[PowerMod[Range[1000], 2, 1000]] (* Vincenzo Librandi, Dec 29 2019 *)

Extensions

More terms and additional comments from Reinhard Zumkeller, Mar 21 2010
Edited by N. J. A. Sloane, Apr 10 2010

A061269 Squares with nonzero digits such that (1) each digit is a square and (2) the sum of the digits is a square.

Original entry on oeis.org

1, 4, 9, 144, 441, 44944
Offset: 1

Views

Author

Amarnath Murthy, Apr 24 2001

Keywords

Comments

Note that (1) implies that the product of the digits is a square.
Next term, if it exists, is > 90000000000. - Larry Reeves (larryr(AT)acm.org), May 11 2001

Examples

			For example, 44944 = 212^2, each digit is a square, sum of digits = 4+4+9+4+4 = 25 = 5^2.

References

  • Amarnath Murthy, The Smarandache multiplicative square sequence is infinite, (to be published in Smarandache Notions Journal).
  • Amarnath Murthy, Infinitely many common members of the Smarandache additive as well as multiplicative square sequence, (to be published in Smarandache Notions Journal).

Links

Crossrefs

If zeros are allowed as digits, the result is A061270.
A subsequence of A006716.
Cf. A053057, A053059, A061267, A061268, A061269, A061270.

Programs

  • Mathematica
    For[n = 1, n < 100000, n++, a := DigitCount[n^2]; If[a[[2]] == 0, If[a[[3]] == 0, If[a[[5]] == 0, If[a[[6]] == 0, If[a[[7]] == 0, If[a[[8]] == 0, If[a[[10]] == 0, If[Sqrt[Sum[a[[i]]*i, {i, 1, 10}]] == Floor[Sqrt[Sum[a[[i]]*i, {i, 1, 10}]]], Print[n^2]]]]]]]]]] (* Stefan Steinerberger, Mar 15 2006 *)

Extensions

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 05 2007

A027675 When squared gives number composed of digits {1,4,9}.

Original entry on oeis.org

1, 2, 3, 7, 12, 21, 38, 107, 212, 31488, 70107, 387288, 95610729, 446653271, 3148717107, 21081079479, 648070211589107021
Offset: 1

Views

Author

Patrick De Geest

Keywords

Comments

If a number has a least significant digit of 0, 4, 5 or 6, it can't be in this sequence. - Alonso del Arte, Jun 11 2016

Examples

			Since 107^2 = 11449, 107 is in the sequence.
As 108^2 = 11664 has two 6's, 108 is not in the sequence.

Links

Crossrefs

Cf. A006716.

Programs

  • Mathematica
    Select[Range[100], Complement[IntegerDigits[#^2], {1, 4, 9}] == {} &] (* Alonso del Arte, Jun 11 2016 *)

A077676 Squares using only squarefree digits (2, 3, 5, 6, 7).

Original entry on oeis.org

25, 36, 225, 256, 576, 625, 676, 5625, 5776, 7225, 27225, 27556, 37636, 55225, 65536, 75625, 225625, 226576, 235225, 265225, 266256, 275625, 276676, 367236, 525625, 553536, 732736, 765625, 767376, 2322576, 2325625, 2356225, 2637376, 2673225
Offset: 1

Views

Author

Amarnath Murthy, Nov 16 2002

Keywords

Comments

a(n) is == 5 or 6 (mod 10).

Links

Crossrefs

Cf. A077674, A077675, A006716. Different from A077437.

Programs

  • Mathematica
    sfdsQ[n_]:=Module[{idn=DigitCount[n]},idn[[1]]==idn[[4]]==idn[[8]] == idn[[9]]==idn[[10]]==0]; Select[Range[2000]^2,sfdsQ] (* Harvey P. Dale, Oct 09 2011 *)
Table[Select[FromDigits/@Tuples[{2,3,5,6,7},n],IntegerQ[Sqrt[#]]&],{n,2,7}]//Flatten (* Harvey P. Dale, Feb 04 2015 *)

Extensions

Corrected and extended by Sascha Kurz, Jan 28 2003

A122988 Number of possible arrangements of the last three digits of x^n for all x>0 (leading zeros omitted).

Original entry on oeis.org

1, 1000, 159, 505, 52, 105, 102, 505, 52, 505, 22, 505, 52, 505, 102, 105, 52, 505, 102, 505, 12, 505, 102, 505, 52, 25, 102, 505, 52, 505, 22, 505, 52, 505, 102, 105, 52, 505, 102, 505, 12, 505, 102, 505, 52, 105, 102, 505, 52, 505, 6, 505, 52, 505, 102, 105, 52
Offset: 0

Views

Author

Sergio Pimentel, Sep 22 2006

Keywords

Comments

Only possible values are {1, 4, 6, 12, 22, 25, 52, 102, 105, 159, 505, 1000}. - Robert G. Wilson v, Sep 27 2006.

Examples

			a(0) = 1 because the last three digits of x^0 are always 001 (just one possibility).
a(100)=4 because the last three digits of x^100 can be 000, 001, 376 or 625 (which is four possibilities).

Links

Crossrefs

Cf. A122986, A122987, A000578, A006716, A027676.

Programs

  • Mathematica
    f[n_] := Length@ Union@ PowerMod[ Range@1000, n, 1000]; Table[ f@n, {n, 0, 56}] (* Robert G. Wilson v *)

Formula

a(n)=1 for n=0 only,
a(n)=4 for n=100*k, k>=1,
a(n)=6 for n=100*k-50, k>=1,
a(n)=12 for n=20*k, k>=1 except if k == 0 (mod 5),
a(n)=22 for n=20*k-10, k>=1 except if k == 3 (mod 5),
a(n)=25 for n=50*k-25, k>=1,
a(n)=52 for n=4*k, k>=1 except if k == 0 (mod 5),
a(n)=102 for n=4*k-2, k>=2 except if k == 3 (mod 5),
a(n)=105 for n=10*k-5, k>=1 except if k == 3 (mod 5),
a(n)=159 for n=2 only,
a(n)=505 for n=2*k-1, k>=2 except if k == 3 (mod 5) and
a(n)=1000 for n=1 only.

Extensions

Edited and extended by Robert G. Wilson v, Sep 27 2006

A119130 Triangular numbers composed of digits {1,4,9}.

Original entry on oeis.org

1, 91, 49141, 144991, 94414411, 941194191, 1194944941, 491919414441, 9999119991411411, 4149449911949149941, 11144994144991949991, 191444491991911949911, 144949944191119411441191, 9449441991199141999494149499499111914141
Offset: 1

Views

Author

Giovanni Resta, May 10 2006

Keywords

Links

Crossrefs

Cf. A000217, A006716, A119131. See A119033 for a table of cross-references.

Formula

a(n) = A000217(A119131(n)). - Tyler Busby, Mar 31 2023

Extensions

a(14) from Max Alekseyev, Aug 15 2013

A136812 Numbers k such that k and k^2 use only the digits 0, 1, 2, 3 and 6.

Original entry on oeis.org

0, 1, 6, 10, 11, 60, 100, 101, 106, 110, 111, 361, 600, 601, 1000, 1001, 1006, 1010, 1011, 1060, 1100, 1101, 1106, 1110, 1631, 3606, 3610, 6000, 6001, 6010, 6011, 10000, 10001, 10006, 10010, 10011, 10060, 10100, 10101, 10106, 10110, 10111, 10301, 10306, 10600, 11000, 11001, 11006, 11010, 11060, 11100, 11101, 16310, 32111, 36060, 36100, 36361
Offset: 1

Views

Author

Jonathan Wellons (wellons(AT)gmail.com), Jan 22 2008

Keywords

Comments

Generated with DrScheme.

Examples

			1031316261^2 = 1063613230203020121.

Links

Crossrefs

Cf. A136808, ..., A137147.
Cf. A006716 = A027675^2, A030174 = A030175^2, A030176 = A030177^2, A058411^2 = A058412, ..., A058473^2 = A058474.
Showing 1-8 of 8 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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