A020332 - OEIS

A020332

Numbers whose base-4 representation is the juxtaposition of two identical strings.

5, 10, 15, 68, 85, 102, 119, 136, 153, 170, 187, 204, 221, 238, 255, 1040, 1105, 1170, 1235, 1300, 1365, 1430, 1495, 1560, 1625, 1690, 1755, 1820, 1885, 1950, 2015, 2080, 2145, 2210, 2275, 2340, 2405, 2470, 2535, 2600, 2665, 2730, 2795, 2860, 2925, 2990

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OFFSET

1,1

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = n*4^floor(log_4(n)+1) + n. - Ilya Gutkovskiy, Jan 26 2018

EXAMPLE

102_10 = 1212_4. - Jon E. Schoenfield, Feb 11 2021

MATHEMATICA

a[n_] := n + n*4^Floor[Log[4, n] + 1]; Array[a, 50] (* Amiram Eldar, Apr 06 2021 *)

b4jQ[n_]:=Module[{idn4=IntegerDigits[n, 4], len}, len=Length[idn4]; EvenQ[len] && Take[ idn4, len/2]==Take[idn4, -len/2]]; Select[Range[3000], b4jQ] (* or *) Table[If[ #[[1]] == 0, Nothing, FromDigits[#, 4]]&/@(Flatten[Join[{#, #}]]&/@Tuples[ {0, 1, 2, 3}, n]), {n, 3}]//Flatten(* Harvey P. Dale, Sep 02 2022 *)

CROSSREFS

Cf. A020330, A020331, A020333, A020334, A020335, A020336, A020337, A020338.

Sequence in context: A067237 A196157 A048703 * A244025 A044830 A033002

Adjacent sequences: A020329 A020330 A020331 * A020333 A020334 A020335

KEYWORD

nonn,base

AUTHOR

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

STATUS

approved