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.

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

Author

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

Keywords

• nonn

Comments

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

Crossrefs

Cf. A298008.

Programs

Mathematica

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

Python

# 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

Formula

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