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

Offset: 1

Author

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

Keywords

• nonn
• base

Examples

			102_10 = 1212_4. - _Jon E. Schoenfield_, Feb 11 2021
		

Links

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

Crossrefs

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

Programs

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 *)

Formula

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