A038822 -id:A038822 - cp's OEIS frontend

A342852 a(n) = A342068(10^n).

2, 5, 5, 7, 8, 12, 33, 52, 93, 236, 479, 1265, 2782, 6650, 15539

Offset: 0

Jon E. Schoenfield, Mar 24 2021

In the table in the Example section, the numbers in the columns for n = 0..9 are the first a(n) terms of A010051, A038800, A038822, ..., A038829, respectively; each column ends at the first term that is greater than the term above it.

a(n) >= a(n-1)/10. - Chai Wah Wu, Mar 25 2021

			Number of primes in the interval [(k-1)*10^n + 1, k*10^n]:
.
   k\n| 0 1  2   3    4    5     6      7       8        9
  ----+---------------------------------------------------
    1 | 0 4 25 168 1229 9592 78498 664579 5761455 50847534
    2 | 1 4 21 135 1033 8392 70435 606028 5317482 47374753
    3 |   2 16 127  983 8013 67883 587252 5173388 46227250
    4 |   2 16 120  958 7863 66330 575795 5084001 45512275
    5 |   3 17 119  930 7678 65367 567480 5019541 44992411
    6 |        114  924 7560 64336 560981 4968836 44591145
    7 |        117  878 7445 63799 555949 4928228 44258984
    8 |             902 7408 63129 551318 4893248 43979302
    9 |                 7323 62712 547572 4863036 43739541
   10 |                 7224 62090 544501 4838319 43529316
   11 |                 7216 61938 541854 4814936 43336106
   12 |                 7224 61543 538339 4792235 43167234
   13 |                      61192 536539 4773628 43014349
   14 |                      60825 534012 4757140 42870136
   15 |                      60627 532197 4741055 42740180
  ... |                        ...    ...     ...      ...
   32 |                      57836 510685 4572164 41368791
   33 |                      57852 510269 4565024 41316074
  ... |                               ...     ...      ...
   51 |                            498385 4475770 40575830
   52 |                            498435 4472349 40547028
  ... |                                       ...      ...
   92 |                                   4357534 39621606
   93 |                                   4360247 39603089
  ... |                                                ...
  235 |                                           38196269
  236 |                                           38197686

Cf. A010051, A038800, A038822, A038823, A038824, A038825, A038826, A038827, A038828, A038829, A342068.

a(10)-a(12) from Chai Wah Wu, Mar 25 2021

a(13)-a(14) from Chai Wah Wu, Mar 31 2021

A298009 a(n) = f(n-1,n)+(n-1)k, n>=1, where the function f(a,b) gives the number of prime numbers in the range [ak,b*k[ with k=10^p. For this sequence we use p=2.

Original entry on oeis.org

25, 121, 216, 316, 417, 514, 616, 714, 815, 914, 1016, 1112, 1215, 1311, 1417, 1512, 1615, 1712, 1812, 1913, 2014, 2110, 2215, 2315, 2410, 2511, 2615, 2714, 2812, 2911, 3012, 3110, 3211, 3315, 3411, 3514, 3613, 3712, 3811, 3911, 4015, 4109, 4216, 4309, 4411, 4512, 4612, 4712, 4808, 4915

Offset: 1

Luis F.B.A. Alexandre, Jan 10 2018

nonn

Realization of the general term presented in the sequence A298008, for the case of p=2. See detailed comments there.

Cf. A298008.

Block[{p = 2, k}, k = 10^p; Array[Apply[Subtract, PrimePi[{k #, k (# - 1)}]] + (# - 1) k &, 50]] (* Michael De Vlieger, Jan 11 2018 *)

# Generates all elements of the sequence smaller than last
last = 1000
p=[2]
c=1
for i in range(3,last+2,2):
    prime = True
    for j in p:
        if i%j == 0:
            prime=False;
            break
    if prime:
        p.append(i)
        c = c + 1
    ii = (i//100)*100
    if i-ii == 1:
        if prime:
            print(ii-100+c-1, end=',')
            c = 1
        else:
            print(ii-100+c, end=',')
            c = 0

a(n) = A038822(n-1) + 100*(n-1); - Michel Marcus, Jan 11 2018

cp's OEIS Frontend

A342852 a(n) = A342068(10^n).

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Extensions

A298009 a(n) = f(n-1,n)+(n-1)k, n>=1, where the function f(a,b) gives the number of prime numbers in the range [ak,b*k[ with k=10^p. For this sequence we use p=2.

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Mathematica

Python

Formula

cp's OEIS Frontend

A342852 a(n) = A342068(10^n).

Views

Author

Keywords

Comments

Examples

Crossrefs

Extensions

A298009 a(n) = f(n-1,n)+(n-1)*k, n>=1, where the function f(a,b) gives the number of prime numbers in the range [a*k,b*k[ with k=10^p. For this sequence we use p=2.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

Python

Formula

A298009 a(n) = f(n-1,n)+(n-1)k, n>=1, where the function f(a,b) gives the number of prime numbers in the range [ak,b*k[ with k=10^p. For this sequence we use p=2.