A020333 Numbers whose base-5 representation is the juxtaposition of two identical strings.

6, 12, 18, 24, 130, 156, 182, 208, 234, 260, 286, 312, 338, 364, 390, 416, 442, 468, 494, 520, 546, 572, 598, 624, 3150, 3276, 3402, 3528, 3654, 3780, 3906, 4032, 4158, 4284, 4410, 4536, 4662, 4788, 4914, 5040, 5166, 5292, 5418, 5544, 5670, 5796, 5922, 6048

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Formula

a(n) = n*5^floor(log_5(n)+1) + n. - Ilya Gutkovskiy, Jan 26 2018

Example

182_10 = 1212_5. - Jon E. Schoenfield, Feb 11 2021

Mathematica

tis5Q[n_]:=Module[{idn=IntegerDigits[n, 5], len}, len=Length[idn]; EvenQ[len] && Take[idn, len/2]==Take[idn, -len/2]]; Select[Range[6500], tis5Q]  (* or *) Flatten[Table[FromDigits[#, 5]&/@Select[(Flatten[{#, #}]&/@Tuples[ Range[ 0, 4], n]), #[[1]]!=0&], {n, 3}]] (* The second program is significantly faster than the first. *) (* Harvey P. Dale, Apr 08 2013 *)
a[n_] := n + n*5^Floor[Log[5, n] + 1]; Array[a, 50] (* Amiram Eldar, Apr 06 2021 *)

Prog

(Python)
from itertools import count, product
def agen():
    for d in count(1):
        for first in "1234":
            for p in product("01234", repeat=d-1):
                yield int((first+"".join(p))*2, 5)
g = agen()
print([next(g) for n in range(1, 49)]) # Michael S. Branicky, Jun 12 2021

Crossrefs

Cf. A020330, A020331, A020332, A020334, A020335, A020336, A020337, A020338.

Sequence in context: A073455 A279894 A209309 * A044831 A033003 A108592

Adjacent sequences: A020330 A020331 A020332 * A020334 A020335 A020336

Keyword

nonn,base

Author

David W. Wilson, Melia Aldridge (ma38(AT)spruce.evansville.edu)

Status

approved