A297710 Partition numbers (A000041) in which parity of digits alternates.

1, 2, 3, 5, 7, 30, 56, 101, 385, 490, 3010, 4565, 8349, 10143

Offset

1,2

Comments

No more terms up to numbpart(7000).

Intersection of A000041 and A030141.

Links

Table of n, a(n) for n=1..14.

Example

8349 is in the sequence because 8, 3, 4 and 9 have even and odd parity alternately.

Prog

(PARI)
is_alt(n) = m=n; e=n%10; n\=10; while(n>0, f=n%10; if(e%2==f%2, return, e=f; n\=10)); return(m)
select(is_alt, vector(7000, n, numbpart(n)))
(Python)
from sympy import npartitions
A297710_list = []
for i in range(1, 10**6):
    n = npartitions(i)
    s = [int(d) for d in str(n)]
    for j in range(len(s)-1):
        if not (s[j]+s[j+1]) % 2:
            break
    else:
        A297710_list.append(n) # Chai Wah Wu, Jan 04 2018

Crossrefs

Cf. A000041, A030141.

Sequence in context: A269022 A174536 A054797 * A287945 A238850 A245064

Adjacent sequences: A297707 A297708 A297709 * A297711 A297712 A297713

Keyword

nonn,base,more

Author

Colin Barker, Jan 04 2018

Status

approved