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A082944
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a(n) = concatenate(n, A010888(2*n), reverse(n)), where A010888 = digital root.
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1
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121, 242, 363, 484, 515, 636, 757, 878, 999, 10201, 11411, 12621, 13831, 14141, 15351, 16561, 17771, 18981, 19291, 20402, 21612, 22822, 23132, 24342, 25552, 26762, 27972, 28282, 29492, 30603
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OFFSET
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1,1
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COMMENTS
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The central digit A010888(2*n) cyclically repeats the nine digits (2, 4, 6, 8, 1, 3, 5, 7, 9) in this order.
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
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REFERENCES
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Amarnath Murthy
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LINKS
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EXAMPLE
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For a(17): 1+7+7+1 = 16. 1+6 = 7. Thus the center digit is 7 and a(17) = 17771.
For a(23): 2+3+3+2 = 10. 1+0 = 1. Thus the center digit is 1 and a(23) = 23132.
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MATHEMATICA
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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 *)
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PROG
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(PARI) A082944(n)=fromdigits(concat([digits(n), (2*n-1)%9+1, Vecrev(digits(n))])) \\ Cf. A010888. - R. J. Cano, Jan 05 2022
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CROSSREFS
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Cf. A010888 (digital root), A004086 (read n backwards: trailing zeros are lost - but not in this sequence here).
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KEYWORD
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easy,nonn,base
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AUTHOR
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Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 06 2003
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EXTENSIONS
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Definition, comment and example corrected by M. F. Hasler, Jan 05 2022
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STATUS
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approved
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