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 1-3 of 3 results.

A028839 Sum of digits of n is a square.

Original entry on oeis.org

1, 4, 9, 10, 13, 18, 22, 27, 31, 36, 40, 45, 54, 63, 72, 79, 81, 88, 90, 97, 100, 103, 108, 112, 117, 121, 126, 130, 135, 144, 153, 162, 169, 171, 178, 180, 187, 196, 202, 207, 211, 216, 220, 225, 234, 243, 252, 259, 261, 268, 270, 277, 286, 295, 301, 306, 310
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

Difference between two consecutive terms is never equal to 8. - Carmine Suriano, Mar 31 2014
In this sequence, there is no number of the form 3*k-1. In other words, if a(n) is not divisible by 9, it must be of the form 3*k+1. - Altug Alkan, Apr 08 2016

Examples

			234511 belongs to the sequence as its sum of digits is 16, a square.

Links

Crossrefs

Cf. A007953, A028837, A050626.
Cf. A053057 (squares whose digit sum is also a square).

Programs

  • Magma
    [n: n in [1..400] | IsSquare(&+Intseq(n))];  // Bruno Berselli, May 26 2011
  • Mathematica
    Select[ Range[ 500 ], IntegerQ[ Sqrt[ Apply[ Plus, IntegerDigits[ # ] ] ] ]& ]
  • PARI
    isok(n) = issquare(sumdigits(n)); \\ Michel Marcus, Oct 30 2014

Extensions

More terms from Erich Friedman

A028845 Iterated product of digits of n is a nonzero square.

Original entry on oeis.org

1, 4, 9, 11, 14, 19, 22, 27, 33, 39, 41, 72, 89, 91, 93, 98, 111, 114, 119, 122, 127, 133, 139, 141, 172, 189, 191, 193, 198, 212, 217, 221, 249, 266, 271, 277, 294, 313, 319, 331, 333, 338, 346, 364, 379, 383, 391, 397, 411, 429, 436, 463, 492, 626, 634, 643
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Examples

			E.g. 27 -> 2*7 = 14 -> 1*4 = 4 is a square.

Links

Crossrefs

Cf. A031347, A050626, A028837.

Programs

  • Mathematica
    ipdQ[n_]:=MemberQ[{9,4,1},NestWhile[Times@@IntegerDigits[#]&,n,#>9&]]; Select[Range[700],ipdQ] (* Harvey P. Dale, Apr 15 2018 *)

Extensions

Extended (and corrected) by Patrick De Geest, Jun 15 1999

A081642 Integers congruent to 0, 1 or 4 (mod 9) which are not squares.

Original entry on oeis.org

10, 13, 18, 19, 22, 27, 28, 31, 37, 40, 45, 46, 54, 55, 58, 63, 67, 72, 73, 76, 82, 85, 90, 91, 94, 99, 103, 108, 109, 112, 117, 118, 126, 127, 130, 135, 136, 139, 145, 148, 153, 154, 157, 162, 163, 166, 171, 172, 175, 180, 181, 184, 189, 190, 193, 198, 199, 202
Offset: 1

Views

Author

Robert G. Wilson v, Mar 26 2003

Keywords

References

  • Mark A. Herkommer, Number Theory, A Programmer's Guide, McGraw-Hill, New York, 1999, page 315.

Crossrefs

Cf. A028837.

Programs

  • Mathematica
    Select[ Range[206], (Mod[ #, 9] == 0 || Mod[ #, 9] == 1 || Mod[ #, 9] == 4) && !IntegerQ[ Sqrt[ # ]] & ]
Select[Flatten[#+{0,1,4}&/@(9*Range[0,30])],!IntegerQ[Sqrt[#]]&] (* Harvey P. Dale, Dec 29 2019 *)
Showing 1-3 of 3 results.

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

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