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.

A118867 Numbers n such that 2^n, 3^n and 5^n have even digit sum.

Original entry on oeis.org

15, 37, 46, 47, 64, 71, 83, 84, 90, 102, 106, 107, 116, 120, 122, 135, 149, 154, 168, 173, 179, 180, 181, 185, 193, 195, 198, 200, 210, 222, 224, 229, 232, 239, 242, 248, 265, 289, 299, 304, 310, 327, 330, 332, 333, 347, 356, 364, 367, 369, 375, 383, 402, 407
Offset: 1

Views

Author

Zak Seidov, May 24 2006

Keywords

Examples

			{2^15,3^15,5^15}={32768,14348907,30517578125} with even digit sum {26,36,44}.

Crossrefs

Subsequence of A118734.

Programs

  • Mathematica
    Select[Range[500],AllTrue[Total/@(IntegerDigits/@{2^#,3^#,5^#}),EvenQ]&] (* Harvey P. Dale, Mar 23 2023 *)
  • PARI
    isok(n) = !(sumdigits(2^n) % 2) && !(sumdigits(3^n) % 2) && !(sumdigits(5^n) % 2); \\ Michel Marcus, Oct 10 2013

A119894 Numbers k such that 2^k, 3^k, 5^k, 7^k and 11^k have even digit sum.

Original entry on oeis.org

64, 90, 106, 168, 181, 185, 229, 242, 369, 407, 447, 470, 481, 503, 552, 568, 583, 612, 648, 657, 683, 684, 742, 758, 804, 811, 852, 863, 896, 915, 924, 928, 1000, 1004, 1068, 1103, 1113, 1126, 1182, 1402, 1410, 1412, 1420, 1428, 1473, 1483, 1484, 1546, 1566
Offset: 1

Views

Author

Zak Seidov, May 26 2006

Keywords

Crossrefs

Cf. A054683, A118734, A118867, A119895, A119896, A119897.

Programs

  • Mathematica
    edsQ[n_]:=And@@EvenQ[Total[IntegerDigits[#]]&/@(Prime[Range[5]]^n)]; Select[Range[1600],edsQ]  (* Harvey P. Dale, Apr 21 2011 *)

A119895 Numbers k such that 2^k, 3^k, 5^k, 7^k, 11^k and 13^k have even digit sum.

Original entry on oeis.org

90, 168, 185, 229, 242, 447, 470, 503, 552, 657, 684, 758, 804, 811, 1000, 1113, 1126, 1182, 1402, 1410, 1412, 1420, 1546, 1566, 1638, 1655, 1663, 1790, 2066, 2180, 2232, 2275, 2362, 2390, 2416, 2504, 2585, 2670, 2721, 2725, 2803, 2814, 2902, 2911, 2928
Offset: 1

Views

Author

Zak Seidov, May 26 2006

Keywords

Links

Crossrefs

Cf. A118734, A118867, A119894, A119896, A119897.

Programs

  • Mathematica
    Select[Range[3000],AllTrue[Total[IntegerDigits[#]]&/@(Prime[ Range[ 6]]^#), EvenQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 10 2018 *)

A119897 Numbers k such that 2^k, 3^k, 5^k, 7^k, 11^k, 13^k, 17^k and 19^k have even digit sum.

Original entry on oeis.org

552, 657, 811, 1412, 1655, 2390, 2504, 2721, 2803, 2902, 3002, 3060, 3135, 3393, 3660, 4414, 4500, 4547, 4750, 4787, 4824, 5036, 5539, 5906, 6782, 7728, 8650, 9263, 9873, 9953, 10367, 10643, 10684, 10723, 11369, 11647, 11867, 11954
Offset: 1

Views

Author

Zak Seidov, May 26 2006

Keywords

Links

Crossrefs

Cf. A054683, A118734, A118867, A119894, A119895, A119896.

Programs

  • Mathematica
    edsQ[n_]:=AllTrue[Prime[Range[8]]^n,EvenQ[Total[IntegerDigits[#]]]&]; Select[ Range[12000],edsQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 10 2017 *)

Extensions

More terms from Harvey P. Dale, May 10 2017

A118730 Numbers k such that 2^k has even digit sum.

Original entry on oeis.org

1, 2, 3, 6, 9, 11, 13, 14, 15, 17, 21, 26, 32, 33, 36, 37, 41, 42, 43, 44, 45, 46, 47, 50, 51, 54, 55, 57, 58, 60, 61, 64, 65, 67, 70, 71, 73, 74, 76, 77, 78, 79, 80, 82, 83, 84, 85, 86, 90, 91, 95, 98, 102, 103, 106, 107, 112, 113, 115, 116, 117, 120, 122, 123, 124, 126
Offset: 1

Views

Author

Zak Seidov, May 22 2006

Keywords

Links

Crossrefs

Cf. A118733, A118734.

Programs

  • Maple
    filter:= proc(n) convert(convert(2^n,base,10),`+`)::even end proc:
select(filter, [$1..1000]); # Robert Israel, Apr 12 2021
  • Mathematica
    Select[Range[126], Mod[ Plus @@ IntegerDigits[2^# ], 2] == 0 &] (* Ray Chandler, Jun 10 2006 *)

A118733 Numbers k such that 3^k has even digit sum.

Original entry on oeis.org

6, 7, 8, 12, 15, 19, 23, 24, 28, 29, 33, 37, 38, 40, 42, 43, 44, 46, 47, 49, 50, 54, 55, 56, 57, 58, 64, 67, 70, 71, 72, 75, 77, 82, 83, 84, 85, 88, 90, 93, 94, 95, 96, 97, 102, 104, 106, 107, 109, 110, 111, 112, 116, 120, 122, 125, 126, 129, 132, 135, 136, 138, 139
Offset: 1

Views

Author

Zak Seidov, May 22 2006

Keywords

Links

Crossrefs

Cf. A004166, A118730, A118734.

Programs

  • Mathematica
    Select[Range[140], Mod[ Plus @@ IntegerDigits[3^# ], 2] == 0 &] (* Ray Chandler, Jun 10 2006 *)
Select[Range[150],EvenQ[Total[IntegerDigits[3^#]]]&] (* Harvey P. Dale, Mar 12 2013 *)
  • Python
    from gmpy2 import digits
def ok(n): return sum(map(int, digits(3**n)))&1 == 0
print([k for k in range(140) if ok(k)]) # Michael S. Branicky, May 11 2025

A119896 Numbers k such that 2^k, 3^k, 5^k, 7^k, 11^k, 13^k and 17^k have even digit sum.

Original entry on oeis.org

90, 185, 447, 470, 503, 552, 657, 758, 804, 811, 1182, 1412, 1546, 1566, 1638, 1655, 2275, 2390, 2504, 2670, 2721, 2803, 2814, 2902, 2928, 3002, 3060, 3087, 3135, 3393, 3660, 3751
Offset: 1

Views

Author

Zak Seidov, May 26 2006

Keywords

Crossrefs

Cf. A054683, A118734, A118867, A119894, A119895, A119897.

A119496 Numbers n such that 2^n, 3^n, 5^n and 7^n have even digit sum.

Original entry on oeis.org

15, 64, 83, 90, 106, 107, 120, 122, 135, 168, 173, 180, 181, 185, 193, 198, 222, 229, 239, 242, 289, 299, 347, 356, 364, 369, 407, 424, 447, 458, 462, 470, 479, 481, 503, 542, 552, 568, 580, 583, 607, 612, 648, 657, 676, 683, 684, 688, 742, 758, 787
Offset: 1

Views

Author

Zak Seidov, May 26 2006

Keywords

Examples

			{2^15,3^15,5^15,7^15}={32768,14348907,30517578125,4747561509943} with even digit sum {26,36,44,64}.

Crossrefs

Subsequence of A118734 and of A118867.

Programs

  • Mathematica
    Select[Range[800],AllTrue[Total/@(IntegerDigits/@({2,3,5,7}^#)),EvenQ]&] (* Harvey P. Dale, Oct 13 2022 *)
  • PARI
    isok(n) = !(sumdigits(2^n) % 2) && !(sumdigits(3^n) % 2) && !(sumdigits(5^n) % 2) && !(sumdigits(7^n) % 2); \\ Michel Marcus, Oct 10 2013
Showing 1-8 of 8 results.

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