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%I #24 Sep 02 2022 14:58:58
%S 5,10,15,68,85,102,119,136,153,170,187,204,221,238,255,1040,1105,1170,
%T 1235,1300,1365,1430,1495,1560,1625,1690,1755,1820,1885,1950,2015,
%U 2080,2145,2210,2275,2340,2405,2470,2535,2600,2665,2730,2795,2860,2925,2990
%N Numbers whose base-4 representation is the juxtaposition of two identical strings.
%H Amiram Eldar, <a href="/A020332/b020332.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = n*4^floor(log_4(n)+1) + n. - _Ilya Gutkovskiy_, Jan 26 2018
%e 102_10 = 1212_4. - _Jon E. Schoenfield_, Feb 11 2021
%t a[n_] := n + n*4^Floor[Log[4, n] + 1]; Array[a, 50] (* _Amiram Eldar_, Apr 06 2021 *)
%t 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 *)
%Y Cf. A020330, A020331, A020333, A020334, A020335, A020336, A020337, A020338.
%K nonn,base
%O 1,1
%A _David W. Wilson_, Melia Aldridge (ma38(AT)spruce.evansville.edu)