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.

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, 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, 3, 17, 1, 219, 1, 2, 4, 10, 1, 2, 1, 1, 46, 1303, 4, 2, 1, 2, 2, 1

Offset: 1

Author

Vladimir Shevelev, Oct 02 2014

Keywords

• nonn
• base

Comments

3^m, m>=1, is of the considered form 3^k*prime, k=m-1>=0, prime=3.

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|,...

Examples

			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.
		

Crossrefs

Cf. A103899, A248146.

Programs

Python

from gmpy2 import is_prime
from itertools import count, islice
def c(n):
    if n < 3: return False
    while n%3 == 0: n //= 3
    return n == 1 or is_prime(n)
def agen(): # generator of terms
    i = 1
    while True:
        s, an = str(i), 1
        while not c(t:=int(s)): i += 2; s += str(i); an += 1
        yield an
        i += 2
print(list(islice(agen(), 78))) # Michael S. Branicky, Oct 05 2024

Extensions

a(43) and beyond from Michael S. Branicky, Oct 05 2024