A372149 Palindrome numbers consisting only of odd digits.

1, 3, 5, 7, 9, 11, 33, 55, 77, 99, 111, 131, 151, 171, 191, 313, 333, 353, 373, 393, 515, 535, 555, 575, 595, 717, 737, 757, 777, 797, 919, 939, 959, 979, 999, 1111, 1331, 1551, 1771, 1991, 3113, 3333, 3553, 3773, 3993, 5115, 5335, 5555, 5775, 5995, 7117, 7337, 7557, 7777, 7997

Offset

1,2

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..1000 from James S. DeArmon)

James S. DeArmon, Common LISP code to create A372149

Mathematica

Select[Range[8000], PalindromeQ[#] && Times@@Boole[OddQ[IntegerDigits[#]]] == 1 &] (* Stefano Spezia, Apr 30 2024 *)
nLP[cn_Integer]:=Module[{s, len, half, left, pal, fdpal}, s=IntegerDigits[cn]; len=Length[s]; half=Ceiling[len/2]; left=Take[s, half]; pal=Join[left, Reverse[Take[left, Floor[len/2]]]]; fdpal=FromDigits[pal]; Which[cn==9, 11, fdpal>cn, fdpal, True, left=IntegerDigits[FromDigits[left]+1]; pal=Join[left, Reverse[Take[left, Floor[len/2]]]]; FromDigits[pal]]]; Select[NestList[nLP[#]&, 1, 200], AllTrue[IntegerDigits[#], OddQ]&] (* Harvey P. Dale, Feb 22 2026 *)

Prog

(Common Lisp) ; See Links section.
(Python)
from itertools import count, islice, product
def agen(): # generator of terms
    for d in count(1):
        for p in product("13579", repeat=d//2):
            left = "".join(p)
            for mid in [[""], "13579"][d&1]:
                yield int(left + mid + left[::-1])
print(list(islice(agen(), 60))) # Michael S. Branicky, Jun 01 2025

Crossrefs

Intersection of A002113 and A014261.

Cf. A056524, A056525.

Sequence in context: A265079 A092361 A029950 * A061507 A046497 A061512

Adjacent sequences: A372146 A372147 A372148 * A372150 A372151 A372152

Keyword

nonn,base

Author

James S. DeArmon, Apr 20 2024

Extensions

Missing 1551 inserted by Stefano Spezia, Apr 30 2024

Status

approved