A118867 -id:A118867 - cp's OEIS frontend

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

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

Zak Seidov, May 26 2006

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

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

Zak Seidov, May 26 2006

Robert Israel, Table of n, a(n) for n = 1..895

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

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

Zak Seidov, May 26 2006

Harvey P. Dale, Table of n, a(n) for n = 1..1600

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

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 *)

More terms from Harvey P. Dale, May 10 2017

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

Zak Seidov, May 26 2006

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

Zak Seidov, May 26 2006

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

Subsequence of A118734 and of A118867.

Select[Range[800],AllTrue[Total/@(IntegerDigits/@({2,3,5,7}^#)),EvenQ]&] (* Harvey P. Dale, Oct 13 2022 *)

isok(n) = !(sumdigits(2^n) % 2) && !(sumdigits(3^n) % 2) && !(sumdigits(5^n) % 2) && !(sumdigits(7^n) % 2); \\ Michel Marcus, Oct 10 2013

cp's OEIS Frontend

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

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

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Mathematica

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.

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

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

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