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.

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

A061868 Numbers n such that n^2 has property that the sum of its digits and the product of its digits are squares (allowing zeros).

Original entry on oeis.org

0, 1, 2, 3, 10, 12, 20, 21, 30, 45, 48, 51, 60, 90, 95, 100, 101, 102, 103, 104, 105, 110, 120, 122, 130, 140, 148, 150, 175, 176, 180, 200, 201, 202, 203, 210, 212, 220, 221, 230, 247, 248, 249, 257, 265, 266, 274, 283, 284, 300, 301, 302, 310, 318, 319, 321
Offset: 1

Views

Author

Larry Reeves (larryr(AT)acm.org), May 11 2001

Keywords

Links

Crossrefs

A061268 does not allow zero product of digits.

Programs

  • Mathematica
    spsQ[n_]:=Module[{idn2=IntegerDigits[n^2]},IntegerQ[Sqrt[Total[idn2]]] && IntegerQ[ Sqrt[Times@@idn2]]]; Select[Range[0,350],spsQ] (* Harvey P. Dale, Dec 12 2013 *)

A061270 Squares such that each digit is a square and the sum of the digits is a square.

Original entry on oeis.org

0, 1, 4, 9, 100, 144, 400, 441, 900, 10000, 10404, 14400, 40000, 40401, 44100, 44944, 90000, 1000000, 1004004, 1040400, 1440000, 4000000, 4004001, 4040100, 4410000, 4494400, 9000000, 9941409, 11909401, 100000000, 100040004, 100400400
Offset: 1

Views

Author

Amarnath Murthy, Apr 24 2001

Keywords

Examples

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

References

  • Amarnath Murthy, Smarandache Additive 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.)
  • Felice Russo, A set of new Smarandache functions, sequences and conjectures in number theory, American Research Press 2000.

Crossrefs

Cf. A053057, A053059, A061267, A061268, A061269.

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), May 11 2001
a(1)=0 inserted by Sean A. Irvine, Jan 29 2023

A053056 Fibonacci numbers whose digit sum is also a Fibonacci number.

Original entry on oeis.org

0, 1, 2, 3, 5, 8, 21, 233, 317811, 3524578, 7778742049, 259695496911122585, 19740274219868223167, 10284720757613717413913, 263621064469290555679241849789653324393054271110084140201023
Offset: 1

Views

Author

Felice Russo, Feb 25 2000

Keywords

Comments

Is this sequence finite?
It is heuristically infinite because of the divergence of the harmonic series. - Charles R Greathouse IV, Sep 20 2012

Examples

			317811 is in the sequence because the sum of its digits 3+1+7+8+1+1=21 is also a Fibonacci number. - Luc Stevens (lms022(AT)yahoo.com), Apr 15 2006

Links

Crossrefs

Cf. A000045, A053056, A061268, A053049.

Programs

  • Maple
    with(combinat): F:=[seq(fibonacci(n),n=2..80)]: a:=proc(n) local ff, sod: ff:=convert(fibonacci(n), base,10): sod:=add(ff[i],i=1..nops(ff)): if member(sod,F)=true then fibonacci(n) else fi end: seq(a(n),n=2..300); # Emeric Deutsch, Apr 17 2006

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Oct 03 2000
More terms from Emeric Deutsch, Apr 17 2006
Edited by R. J. Mathar, Aug 08 2008

A061272 Squares such that (1) each digit is a square, (2) the sum of squares of the digits is a square.

Original entry on oeis.org

0, 1, 4, 9, 100, 400, 900, 1444, 10000, 40000, 90000, 144400, 1000000, 4000000, 9000000, 14440000, 94109401, 100000000, 400000000, 900000000, 1444000000, 9410940100, 10000000000, 10100049001, 40000000000, 90000000000, 144400000000, 414441100441, 941094010000
Offset: 1

Views

Author

Amarnath Murthy, Apr 24 2001

Keywords

Examples

			1444 = 38^2, each digit is a square, Sum of the squares of digits = 1+16+16+16 = 49 = 7^2.

References

  • Amarnath Murthy, Smarandache Pythagoras Additive Square Sequence. (To be published in Smarandache Notions Journal).

Crossrefs

Cf. A053057, A053059, A061267, A061268, A061269, A061270, A061090.

Programs

  • Mathematica
    okQ[n_]:=Module[{fd=FromDigits[n]},IntegerQ[Sqrt[fd]]&&IntegerQ[ Sqrt[ Total[n^2]]]]; FromDigits/@Select[Tuples[{0,1,4,9},8],okQ] (* Harvey P. Dale, May 12 2011 *)

Extensions

Corrected and extended by Harvey P. Dale, May 12 2011
More terms from Jason Yuen, Aug 27 2025
Showing 1-5 of 5 results.

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

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