A323744 Triangle read by rows: T(n,k) is the number of primes in the half-open interval [10^n, 10^n + 10^k), n >= 1, 1 <= k <= n.

4, 4, 21, 1, 16, 135, 2, 11, 106, 1033, 1, 6, 81, 861, 8392, 1, 6, 75, 753, 7216, 70435, 0, 2, 61, 614, 6241, 61938, 606028, 1, 6, 54, 551, 5411, 54208, 541854, 5317482, 2, 7, 49, 487, 4832, 48155, 482449, 4814936, 47374753, 0, 5, 44, 406, 4306, 43427, 434650, 4341930, 43336106, 427154205

Offset

1,1

Comments

T(n,k) is the number of primes among the first 10^k (n-1)-digit numbers.

Columns (see Example section) illustrate the decreasing density of primes.

Links

Table of n, a(n) for n=1..55.

Formula

T(n,k) = A000720(10^n + 10^k - 1) - A000720(10^n - 1) = A000720(10^n + 10^k) - A000720(10^n).

T(n,k) = A000720(10^n + 10^k) - A006880(n).

Example

Table begins
  n\k| 1  2   3    4    5     6      7       8        9
-----+-------------------------------------------------
   1 | 4
   2 | 4 21
   3 | 1 16 135
   4 | 2 11 106 1033
   5 | 1  6  81  861 8392
   6 | 1  6  75  753 7216 70435
   7 | 0  2  61  614 6241 61938 606028
   8 | 1  6  54  551 5411 54208 541854 5317482
   9 | 2  7  49  487 4832 48155 482449 4814936 47374753
  10 | 0  5  44  406 4306 43427 434650 4341930 43336106
  11 | 1  7  47  394 4019 39434 394401 3948161 39475591
  12 | 0  4  37  335 3614 36249 361726 3618282 36190991
  13 | 0  3  34  354 3382 33456 334312 3342093 33405006
  14 | 0  4  30  304 3045 30892 310582 3102679 31019409
  15 | 0  2  24  263 2805 28845 289394 2893937 28946421
  16 | 0  4  20  270 2697 27168 271897 2714904 27153205
  17 | 1  7  27  265 2515 25463 255085 2555873 25549226

Crossrefs

Cf. A000040, A000720, A006880.

k=2 column is A093538 (after that sequence's 1st 2 terms).

Sequence in context: A191366 A216164 A270376 * A205142 A072696 A075219

Adjacent sequences: A323741 A323742 A323743 * A323745 A323746 A323747

Keyword

nonn,tabl

Author

Jon E. Schoenfield, Apr 13 2019

Status

approved