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

Author

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

Keywords

• nonn
• base

Examples

			182_10 = 1212_5. - _Jon E. Schoenfield_, Feb 11 2021
		

Links

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

Crossrefs

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

Programs

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 *)

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

Formula

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