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

1,1

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|,...

Links

Table of n, a(n) for n=1..85.

Example

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.

Prog

(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

Crossrefs

Cf. A103899, A248146.

Sequence in context: A069347 A161606 A300362 * A171398 A113607 A351352

Adjacent sequences: A248142 A248143 A248144 * A248146 A248147 A248148

Keyword

nonn,base

Author

Vladimir Shevelev, Oct 02 2014

Extensions

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

Status

approved