A156230 -id:A156230 - cp's OEIS frontend

A244158 If n = Sum c_i * 10^i then a(n) = Sum c_i * Cat(i+1), where Cat(k) = A000108(k).

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 5

Offset: 0

Antti Karttunen, Jun 22 2014

This sequence converts any number from various "Catalan Base number systems" (when represented as decimal numbers) back to the integer the numeral represents: e.g. we have a(A014418(n)) = n and a(A244159(n)) = n (except for the latter this is eventually broken by the shortcomings of the decimal representation used, while for the former it works for all n, because no digits larger than 3 will ever appear in the terms of A014418).
A197433 is similar, but replaces 2^k with A000108(k+1) in binary expansion of n.
For 1- and 2-digit numbers the same as A156230. - R. J. Mathar, Jun 27 2014

Index entries for sequences related to decimal expansion of n

Cf. A000108, A014418, A244159, A197433, A244155, A244156, A244157.

Differs from A028897 and A081594 for the first time at n=100, which here is a(100) = 5.

A244158 := proc(n)
    local dgs,k ;
    dgs := convert(n,base,10) ;
    add( op(k,dgs)*A000108(k),k=1..nops(dgs)) ;
end proc: # R. J. Mathar, Jan 31 2015

A081594 Let n = 10x + y where 0 <= y <= 9, x >= 0. Then a(n) = 2x+y.

Original entry on oeis.org

Offset: 0

N. J. A. Sloane, Apr 22 2003

Vincenzo Librandi, Table of n, a(n) for n = 0..2000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,1,-1).

Cf. A081502. Differs from A028897, A156230 and A244158 for the first time at n=100, which here is a(100) = 20.

[(n+4*y)/5 where y is n mod 10: n in [0..100]]; // Bruno Berselli, Jun 24 2014

A081594:=n->n-8*floor(n/10); seq(A081594(n), n=0..100); # Wesley Ivan Hurt, Jun 25 2014

CoefficientList[Series[-x (7 x^9 - x^8 - x^7 - x^6 - x^5 - x^4 - x^3 - x^2 - x - 1)/((x - 1)^2 (x + 1) (x^4 - x^3 + x^2 - x+1) (x^4 + x^3 + x^2 + x + 1)), {x, 0, 150}], x] (* Vincenzo Librandi, Jun 25 2014 *)
LinearRecurrence[{1,0,0,0,0,0,0,0,0,1,-1},{0,1,2,3,4,5,6,7,8,9,2},110] (* or *) Table[Range[n,n+9],{n,0,26,2}]//Flatten (* Harvey P. Dale, Jul 22 2021 *)

my(n, x, y); vector(200, n, y=(n-1)%10; x=(n-1-y)\10; 2*x+y) \\ Colin Barker, Jun 24 2014

[n-8*floor(n/10) for n in (0..100)] # Bruno Berselli, Jun 24 2014

a(n) = (2 * floor(n/10)) + (n modulo 10). - Antti Karttunen, Jun 22 2014
G.f.: -x*(7*x^9 -x^8 -x^7 -x^6 -x^5 -x^4 -x^3 -x^2 -x -1) / ((x -1)^2*(x +1)*(x^4 -x^3 +x^2 -x +1)*(x^4 +x^3 +x^2 +x +1)). - Colin Barker, Jun 23 2014
a(n) = n - 8*floor(n/10). [Bruno Berselli, Jun 24 2014]

Terms up to n=100 added by Antti Karttunen, Jun 22 2014

G.f. revised by Vincenzo Librandi, Jun 25 2014

cp's OEIS Frontend

A244158 If n = Sum c_i * 10^i then a(n) = Sum c_i * Cat(i+1), where Cat(k) = A000108(k).

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A081594 Let n = 10x + y where 0 <= y <= 9, x >= 0. Then a(n) = 2x+y.

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