cp's OEIS Frontend

A248145 Consider the partition of the positive odd integers into minimal blocks such that concatenation of numbers in each block is a number of the form 3^k*prime, k>=0. Sequence lists numbers of odd integers in the blocks.

%I A248145 #45 Oct 05 2024 08:56:28
%S A248145 2,1,1,1,1,1,1,1,1,1,1,3,1,1,2,1,1,1,1,1,2,1,2,1,1,1,3,1,1,2,1,1,1,7,
%T A248145 1,1,1,2,1,1,1,2,6,1,5,11,7,1,1,1,2,1,1,1,2,1,1,348,2,20,30,453,2,1,2,
%U A248145 3,17,1,219,1,2,4,10,1,2,1,1,46,1303,4,2,1,2,2,1
%N A248145 Consider the partition of the positive odd integers into minimal blocks such that concatenation of numbers in each block is a number of the form 3^k*prime, k>=0. Sequence lists numbers of odd integers in the blocks.
%C A248145 3^m, m>=1, is of the considered form 3^k*prime, k=m-1>=0, prime=3.
%C A248145 The first blocks of the partition are |1,3|,|5|,|7|,|9|,|11|,|13|,|15|,|17|,|19|,|21|,|23|,|25,27,29|,|31|,|33|,|35,37|,...
%e A248145 The 12th block of partition is |25,27,29|, since we have 25=5^2, 2527=7*19^2, 252729=3^2*28081, and only the last number is of the required form. So a(12)=3.
%o A248145 (Python)
%o A248145 from gmpy2 import is_prime
%o A248145 from itertools import count, islice
%o A248145 def c(n):
%o A248145     if n < 3: return False
%o A248145     while n%3 == 0: n //= 3
%o A248145     return n == 1 or is_prime(n)
%o A248145 def agen(): # generator of terms
%o A248145     i = 1
%o A248145     while True:
%o A248145         s, an = str(i), 1
%o A248145         while not c(t:=int(s)): i += 2; s += str(i); an += 1
%o A248145         yield an
%o A248145         i += 2
%o A248145 print(list(islice(agen(), 78))) # _Michael S. Branicky_, Oct 05 2024
%Y A248145 Cf. A103899, A248146.
%K A248145 nonn,base
%O A248145 1,1
%A A248145 _Vladimir Shevelev_, Oct 02 2014
%E A248145 a(43) and beyond from _Michael S. Branicky_, Oct 05 2024