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%I #20 Jan 06 2022 20:42:14
%S 121,242,363,484,515,636,757,878,999,10201,11411,12621,13831,14141,
%T 15351,16561,17771,18981,19291,20402,21612,22822,23132,24342,25552,
%U 26762,27972,28282,29492,30603
%N a(n) = concatenate(n, A010888(2*n), reverse(n)), where A010888 = digital root.
%C The central digit A010888(2*n) cyclically repeats the nine digits (2, 4, 6, 8, 1, 3, 5, 7, 9) in this order.
%C The sum of the digits of n plus the digits of the reverse of n is always simply 2 times the sum of the digits of n. - _Harvey P. Dale_, Aug 12 2019
%D Amarnath Murthy
%e For a(17): 1+7+7+1 = 16. 1+6 = 7. Thus the center digit is 7 and a(17) = 17771.
%e For a(23): 2+3+3+2 = 10. 1+0 = 1. Thus the center digit is 1 and a(23) = 23132.
%t nxt[n_]:=Module[{idn=IntegerDigits[n],b,c},b=NestWhile[Total[IntegerDigits[ # ]]&, 2 Total[idn],#>9&];c=Reverse[idn];FromDigits[Join[idn,{b},c]]]; Table[ nxt[n],{n,20}] (* _Harvey P. Dale_, Aug 12 2019 *)
%o (PARI) A082944(n)=fromdigits(concat([digits(n), (2*n-1)%9+1, Vecrev(digits(n))])) \\ Cf. A010888. - _R. J. Cano_, Jan 05 2022
%Y Cf. A010888 (digital root), A004086 (read n backwards: trailing zeros are lost - but not in this sequence here).
%K easy,nonn,base
%O 1,1
%A Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 06 2003
%E Definition, comment and example corrected by _M. F. Hasler_, Jan 05 2022
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