cp's OEIS Frontend

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.

%I A298009 #17 May 24 2021 08:00:07
%S A298009 25,121,216,316,417,514,616,714,815,914,1016,1112,1215,1311,1417,1512,
%T A298009 1615,1712,1812,1913,2014,2110,2215,2315,2410,2511,2615,2714,2812,
%U A298009 2911,3012,3110,3211,3315,3411,3514,3613,3712,3811,3911,4015,4109,4216,4309,4411,4512,4612,4712,4808,4915
%N 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.
%C A298009 Realization of the general term presented in the sequence A298008, for the case of p=2. See detailed comments there.
%F A298009 a(n) = A038822(n-1) + 100*(n-1); - _Michel Marcus_, Jan 11 2018
%t A298009 Block[{p = 2, k}, k = 10^p; Array[Apply[Subtract, PrimePi[{k #, k (# - 1)}]] + (# - 1) k &, 50]] (* _Michael De Vlieger_, Jan 11 2018 *)
%o A298009 (Python)
%o A298009 # Generates all elements of the sequence smaller than last
%o A298009 last = 1000
%o A298009 p=[2]
%o A298009 c=1
%o A298009 for i in range(3,last+2,2):
%o A298009     prime = True
%o A298009     for j in p:
%o A298009         if i%j == 0:
%o A298009             prime=False;
%o A298009             break
%o A298009     if prime:
%o A298009         p.append(i)
%o A298009         c = c + 1
%o A298009     ii = (i//100)*100
%o A298009     if i-ii == 1:
%o A298009         if prime:
%o A298009             print(ii-100+c-1, end=',')
%o A298009             c = 1
%o A298009         else:
%o A298009             print(ii-100+c, end=',')
%o A298009             c = 0
%Y A298009 Cf. A298008.
%K A298009 nonn
%O A298009 1,1
%A A298009 _Luis F.B.A. Alexandre_, Jan 10 2018