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