A178447 -id:A178447 - cp's OEIS frontend

A177868 a(n) = number of 2-digit primes with digit sum n, where n runs through the non-multiples of 3 in the range [2..17].

1, 2, 2, 2, 3, 3, 3, 1, 1, 2, 1

Offset: 1

N. J. A. Sloane, Dec 28 2010

			Digital sums of 2-digit primes
Sum     count
2       1
4       2
5       2
7       2
8       3
10      3
11      3
13      1
14      1
16      2
17      1

Table of n, a(n) for n = 1..11
BigPrimes.net, Digit sums of primes

For 2- through 9-digit primes the counts are in A177868, A178183, A178447, A178571, A178605, A178876, A178879, A178884.

Cf. 2nd row of A178701.

A178183 a(n) = number of 3-digit primes with digit sum n, where n runs through the non-multiples of 3 in the range [2..26].

Original entry on oeis.org

1, 2, 4, 7, 7, 12, 13, 16, 16, 13, 18, 12, 11, 6, 4, 1, 0

Offset: 1

N. J. A. Sloane, Dec 28 2010

			Digit-sums of 3-digit primes
Sum     count
2       1
4       2
5       4
7       7
8       7
10      12
11      13
13      16
14      16
16      13
17      18
19      12
20      11
22      6
23      4
25      1
26      0

BigPrimes.net, Digit sums of primes

For 2- through 9-digit primes the counts are in A177868, A178183, A178447, A178571, A178605, A178876, A178879, A178884.

Cf. 3rd row of A178701.

Join[SortBy[Tally[Total[IntegerDigits[#]]&/@Prime[Range[26,168]]],First][[;;,2]],{0}] (* Harvey P. Dale, Feb 08 2025 *)

A178884 a(n) = number of 9-digit primes with digit sum n, where n runs through the non-multiples of 3 in the range [2..80].

Original entry on oeis.org

0, 2, 26, 226, 372, 1457, 3312, 9159, 13320, 32077, 50752, 102027, 138554, 249053, 331920, 535444, 655423, 966278, 1152057, 1546854, 1751100, 2168566, 2374001, 2719026, 2850784, 3029814, 3063907, 3019100, 2943918, 2691740, 2519884, 2134422, 1930862, 1511648, 1303187, 935353, 783315, 514221, 402227, 238252, 182466, 97415, 66012, 30140, 21162, 8438, 4350, 1311, 906, 170, 65, 3, 1

Offset: 1

N. J. A. Sloane, Dec 28 2010

			Digit-sums of 9-digit primes
Sum     count
2       0
4       2
5       26
7       226
8       372
10      1457
11      3312
13      9159
14      13320
16      32077
17      50752
19      102027
20      138554
22      249053
23      331920
25      535444
26      655423
28      966278
29      1152057
31      1546854
32      1751100
34      2168566
...

BigPrimes.net, Digit sums of primes

For 2- through 9-digit primes the counts are in A177868, A178183, A178447, A178571, A178605, A178876, A178879, A178884.

A178701 An irregular array read by rows. The k-th entry of row r is the number of r-digit primes with digit sum k.

Original entry on oeis.org

1, 0, 1, 1, 0, 1, 2, 2, 2, 3, 3, 3, 1, 1, 2, 1, 1, 2, 4, 7, 7, 12, 13, 16, 16, 13, 18, 12, 11, 6, 4, 1, 0, 0, 4, 8, 20, 19, 31, 52, 67, 77, 93, 101, 116, 95, 92, 91, 63, 51, 29, 30, 16, 5, 0, 1, 0, 4, 12, 28, 45, 95, 143, 236, 272, 411, 479, 630, 664, 742, 757, 741, 706, 580, 528, 379, 341, 205, 166, 84, 62, 34, 13, 4, 2, 0, 2, 14, 58, 76, 204, 389, 660, 852, 1448, 1971, 2832, 3101, 4064, 4651, 5393, 5376, 5570, 5785, 5287, 4796

Offset: 1

Robert G. Wilson v, Dec 29 2010

Each row, r, has 6r-1 terms. The first row does not account for the prime 3 and its count of 1.

			To begin the second row, only 11 has digit-sum 2, so the first term is 1; both 13 & 31 have digit-sum 4 so the second term is 2; both 23 & 41 have digit-sum 5, so the third term is 2; etc.
To begin the third row, only 101 -> 2, so its first term is 1, both 103 & 211 -> 4 so its second term is 2; 113, 131, 311 & 401 -> 5, so its third term is 4; etc.
  \k 2, 4,  5,  7,  8,  10,  11,  13,  14,   16,   17,   19,   20,   22,   23,   25,   26, ...
  r\
  1: 1, 0,  1,  1,  0;
  2: 1, 2,  2,  2,  3,   3,   3,   1,   1,    2,    1;
  3: 1, 2,  4,  7,  7,  12,  13,  16,  16,   13,   18,   12,   11,    6,    4,    1,    0;
  4: 0, 4,  8, 20, 19,  31,  52,  67,  77,   93,  101,  116,   95,   92,   91,   63,   51, ...
  5: 0, 4, 12, 28, 45,  95, 143, 236, 272,  411,  479,  630,  664,  742,  757,  741,  706, ...
  6: 0, 2, 14, 58, 76, 204, 389, 660, 852, 1448, 1971, 2832, 3101, 4064, 4651, 5393, 5376, ...
etc.

Robert G. Wilson v, Table of n, a(n) for n = 1..320
Craig Mayhew, Sums of digits of primes

Cf. A000040, A006880, A007605, A177868, A178183, A178447, A178571, A178605, A178876, A178879, A178884.

Row sums (except for the first term) give A006879. The indices k are given by A001651 (beginning with 2).

dir[n_] := Floor[(3 n + 2)/2]; inv[n_] := Floor[(2 n - 1)/3]; f[n_] := Block[{p = NextPrime[10^(n - 1)], t = Table[0, {inv[9 n]}]}, While[p < 10^n, t[[ inv[Plus @@ IntegerDigits@ p]]]++; p = NextPrime@ p]; t]; Array[f, 5] // Flatten

cp's OEIS Frontend

A177868 a(n) = number of 2-digit primes with digit sum n, where n runs through the non-multiples of 3 in the range [2..17].

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A178183 a(n) = number of 3-digit primes with digit sum n, where n runs through the non-multiples of 3 in the range [2..26].

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A178884 a(n) = number of 9-digit primes with digit sum n, where n runs through the non-multiples of 3 in the range [2..80].

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A178701 An irregular array read by rows. The k-th entry of row r is the number of r-digit primes with digit sum k.

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Mathematica