A237346 -id:A237346 - cp's OEIS frontend

A235499 For k in {2,3,...,9} define a sequence as follows: a(0)=0; for n>=0, a(n+1)=a(n)+1, unless a(n) ends in k, in which case a(n+1) is obtained by replacing the last digit of a(n) with the digit(s) of k^2. This is k(3).

0, 1, 2, 3, 9, 10, 11, 12, 13, 19, 20, 21, 22, 23, 29, 30, 31, 32, 33, 39, 40, 41, 42, 43, 49, 50, 51, 52, 53, 59, 60, 61, 62, 63, 69, 70, 71, 72, 73, 79, 80, 81, 82, 83, 89, 90, 91, 92, 93, 99, 100, 101, 102, 103, 109, 110, 111, 112, 113, 119, 120, 121, 122, 123, 129

Offset: 0

Vincenzo Librandi, Feb 06 2014

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,-1).

Cf. A235498, A237341, A237342, A237343, A237344, A237345, A237346.

CoefficientList[Series[(x^5 + 6 x^4 + x^3 + x^2 + x)/(x^6 - x^5 - x + 1), {x, 0, 50}], x] (* Vincenzo Librandi, Feb 08 2014 *)
nxt[n_]:=If[Mod[n,10]==3,FromDigits[Join[Most[IntegerDigits[n]],{9}]], n+ 1]; NestList[nxt,0,70] (* or *) LinearRecurrence[{1,0,0,0,1,-1},{0,1,2,3,9,10},70] (* Harvey P. Dale, Oct 02 2016 *)

G.f.: (x^5+6*x^4+x^3+x^2+x)/(x^6-x^5-x+1). - Alois P. Heinz, Feb 07 2014

Definition by N. J. A. Sloane, Feb 07 2014

A237341 For k in {2,3,...,9} define a sequence as follows: a(0)=0; for n>=0, a(n+1)=a(n)+1, unless a(n) ends in k, in which case a(n+1) is obtained by replacing the last digit of a(n) with the digit(s) of k^2. This is k(4).

Original entry on oeis.org

0, 1, 2, 3, 4, 16, 17, 18, 19, 20, 21, 22, 23, 24, 216, 217, 218, 219, 220, 221, 222, 223, 224, 2216, 2217, 2218, 2219, 2220, 2221, 2222, 2223, 2224, 22216, 22217, 22218, 22219, 22220, 22221, 22222, 22223, 22224, 222216, 222217, 222218, 222219, 222220, 222221

Offset: 0

Vincenzo Librandi, Feb 06 2014

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, -10).

Cf. A235498, A235499, A237341 - A237346.

G.f.: (10*x^17 +20*x^16 +30*x^15 +40*x^14 -20*x^13 -10*x^12 +10*x^10 +20*x^9 +19*x^8 +18*x^7 +17*x^6 +16*x^5 +4*x^4 +3*x^3 +2*x^2 +x)/(10*x^18 -11*x^9 +1). - Alois P. Heinz, Feb 07 2014

Definition by N. J. A. Sloane, Feb 07 2014

A235498 For k in {2,3,...,9} define a sequence as follows: a(0)=0; for n>=0, a(n+1)=a(n)+1, unless a(n) ends in k, in which case a(n+1) is obtained by replacing the last digit of a(n) with the digit(s) of k^2. This is k(2).

Original entry on oeis.org

0, 1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74

Offset: 0

Vincenzo Librandi, Feb 06 2014

An alternative and simpler definition: numbers not ending in 3. - Charles R Greathouse IV, Feb 07 2014

Subsequence of A052405.

Cf. A235499, A237341 - A237346.

G.f.: (x^9 +x^8 +x^7 +x^6 +x^5 +x^4 +2*x^3 +x^2 +x) / (x^10 -x^9 -x +1). - Alois P. Heinz, Feb 07 2014

Definition by N. J. A. Sloane, Feb 07 2014

A237344 For k in {2,3,...,9} define a sequence as follows: a(0)=0; for n>=0, a(n+1)=a(n)+1, unless a(n) ends in k, in which case a(n+1) is obtained by replacing the last digit of a(n) with the digit(s) of k^2. This is k(7).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 49, 50, 51, 52, 53, 54, 55, 56, 57, 549, 550, 551, 552, 553, 554, 555, 556, 557, 5549, 5550, 5551, 5552, 5553, 5554, 5555, 5556, 5557, 55549, 55550, 55551, 55552, 55553, 55554, 55555, 55556, 55557, 555549, 555550, 555551, 555552

Offset: 0

Vincenzo Librandi, Feb 06 2014

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, -10).

Cf. A235498, A235499, A237341 - A237346.

CoefficientList[Series[(10 x^17 - 20 x^16 - 10 x^15 + 10 x^13 + 20 x^12 + 30 x^11 + 40 x^10 + 50 x^9 + 49 x^8 + 7 x^7 + 6 x^6 + 5 x^5 + 4 x^4 + 3 x^3 + 2 x^2 + x)/(10 x^18 -11 x^9 + 1), {x, 0, 50}], x] (* Vincenzo Librandi, Sep 24 2014 *)

G.f.: (10*x^17 -20*x^16 -10*x^15 +10*x^13 +20*x^12 +30*x^11 +40*x^10 +50*x^9 +49*x^8 +7*x^7 +6*x^6 +5*x^5 +4*x^4 +3*x^3 +2*x^2 +x)/(10*x^18 -11*x^9 +1). - Alois P. Heinz, Feb 07 2014

Definition by N. J. A. Sloane, Feb 07 2014

A237415 For k in {2,3,...,9} define a sequence as follows: a(0)=0; for n>=0, a(n+1)=a(n)+1, unless a(n) ends in k, in which case a(n+1) is obtained by replacing the last digit of a(n) with the digit(s) of k^3. This is k(2).

Original entry on oeis.org

0, 1, 2, 8, 9, 10, 11, 12, 18, 19, 20, 21, 22, 28, 29, 30, 31, 32, 38, 39, 40, 41, 42, 48, 49, 50, 51, 52, 58, 59, 60, 61, 62, 68, 69, 70, 71, 72, 78, 79, 80, 81, 82, 88, 89, 90, 91, 92, 98, 99, 100, 101, 102, 108, 109, 110, 111, 112, 118, 119, 120, 121, 122, 128

Offset: 0

Vincenzo Librandi, Feb 07 2014

Nonnegative integers m such that floor(2*m^2/10) = 2*floor(m^2/10). [Bruno Berselli, Dec 08 2015]

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,-1).

Cf. A235498, A235499, A237341 - A237346.

I:=[0,1,2,8,9,10]; [n le 6 select I[n] else Self(n-1)+Self(n-5)-Self(n-6): n in [1..80]]; // Vincenzo Librandi, Feb 12 2014

LinearRecurrence[{1, 0, 0, 0, 1, -1}, {0, 1, 2, 8, 9, 10}, 70] (* Bruno Berselli, Feb 08 2014 *)
CoefficientList[Series[x (1 + x + 6 x^2 + x^3 + x^4)/((1 - x)^2 (1 + x + x^2 + x^3 + x^4)), {x, 0, 100}], x] (* Vincenzo Librandi, Feb 12 2014 *)
NestList[If[Mod[#,10]==2,FromDigits[Join[Most[IntegerDigits[#]],{8}]], #+ 1]&,0,100] (* Harvey P. Dale, Feb 21 2016 *)

G.f.: x*(1 + x + 6*x^2 + x^3 + x^4)/((1 - x)^2*(1 + x + x^2 + x^3 + x^4)). [Bruno Berselli, Feb 08 2014]

a(n) = a(n-1)+a(n-5)-a(n-6). - Vincenzo Librandi, Feb 12 2014

Definition by N. J. A. Sloane, Feb 07 2014

A237342 For k in {2,3,...,9} define a sequence as follows: a(0)=0; for n>=0, a(n+1)=a(n)+1, unless a(n) ends in k, in which case a(n+1) is obtained by replacing the last digit of a(n) with the digit(s) of k^2. This is k(5).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 25, 225, 2225, 22225, 222225, 2222225, 22222225, 222222225, 2222222225, 22222222225, 222222222225, 2222222222225, 22222222222225, 222222222222225, 2222222222222225, 22222222222222225, 222222222222222225, 2222222222222222225

Offset: 0

Vincenzo Librandi, Feb 06 2014

Index entries for linear recurrences with constant coefficients, signature (11, -10).

Cf. A235498, A235499, A237341 - A237346.

Join[Range[0, 4], Table[(25 + 2 10^(n - 4))/9, {n, 5, 30}]] (* Bruno Berselli, Feb 08 2014 *)

G.f.: (10*x^6-9*x^5-9*x^4-9*x^3-9*x^2+x)/(10*x^2-11*x+1). - Alois P. Heinz, Feb 07 2014

a(n) = ( 25 + 2*10^(n-4) )/9 for n>4. [Bruno Berselli, Feb 08 2014]

Definition by N. J. A. Sloane, Feb 07 2014

A237343 For k in {2,3,...,9} define a sequence as follows: a(0)=0; for n>=0, a(n+1)=a(n)+1, unless a(n) ends in k, in which case a(n+1) is obtained by replacing the last digit of a(n) with the digit(s) of k^2. This is k(6).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 36, 336, 3336, 33336, 333336, 3333336, 33333336, 333333336, 3333333336, 33333333336, 333333333336, 3333333333336, 33333333333336, 333333333333336, 3333333333333336, 33333333333333336, 333333333333333336, 3333333333333333336

Offset: 0

Vincenzo Librandi, Feb 06 2014

Index entries for linear recurrences with constant coefficients, signature (11, -10).

Cf. A235498, A235499, A237341 - A237346.

Join[Range[0, 5], Table[(8 + 10^(n - 5))/3, {n, 6, 30}]] (* Bruno Berselli, Feb 08 2014 *)

G.f.: (20*x^7-9*x^6-9*x^5-9*x^4-9*x^3-9*x^2+x)/(10*x^2-11*x+1). - Alois P. Heinz, Feb 07 2014

a(n) = ( 8 + 10^(n-5) )/3 for n>5. [Bruno Berselli, Feb 08 2014]

Definition by N. J. A. Sloane, Feb 07 2014

A237345 For k in {2,3,...,9} define a sequence as follows: a(0)=0; for n>=0, a(n+1)=a(n)+1, unless a(n) ends in k, in which case a(n+1) is obtained by replacing the last digit of a(n) with the digit(s) of k^2. This is k(8).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 64, 65, 66, 67, 68, 664, 665, 666, 667, 668, 6664, 6665, 6666, 6667, 6668, 66664, 66665, 66666, 66667, 66668, 666664, 666665, 666666, 666667, 666668, 6666664, 6666665, 6666666, 6666667, 6666668, 66666664, 66666665, 66666666

Offset: 0

Vincenzo Librandi, Feb 06 2014

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 11, 0, 0, 0, 0, -10).

Cf. A235498, A235499, A237341 - A237346.

G.f.: -(10*x^13 +10*x^12 +10*x^11 +10*x^10 +20*x^9 -25*x^8 -15*x^7 -5*x^6 +5*x^5 +4*x^4 +3*x^3 +2*x^2+x)/(-10*x^10+11*x^5-1). - Alois P. Heinz, Feb 07 2014

Definition by N. J. A. Sloane, Feb 07 2014

cp's OEIS Frontend

A235499 For k in {2,3,...,9} define a sequence as follows: a(0)=0; for n>=0, a(n+1)=a(n)+1, unless a(n) ends in k, in which case a(n+1) is obtained by replacing the last digit of a(n) with the digit(s) of k^2. This is k(3).

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A237341 For k in {2,3,...,9} define a sequence as follows: a(0)=0; for n>=0, a(n+1)=a(n)+1, unless a(n) ends in k, in which case a(n+1) is obtained by replacing the last digit of a(n) with the digit(s) of k^2. This is k(4).

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A235498 For k in {2,3,...,9} define a sequence as follows: a(0)=0; for n>=0, a(n+1)=a(n)+1, unless a(n) ends in k, in which case a(n+1) is obtained by replacing the last digit of a(n) with the digit(s) of k^2. This is k(2).

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A237344 For k in {2,3,...,9} define a sequence as follows: a(0)=0; for n>=0, a(n+1)=a(n)+1, unless a(n) ends in k, in which case a(n+1) is obtained by replacing the last digit of a(n) with the digit(s) of k^2. This is k(7).

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Mathematica

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A237415 For k in {2,3,...,9} define a sequence as follows: a(0)=0; for n>=0, a(n+1)=a(n)+1, unless a(n) ends in k, in which case a(n+1) is obtained by replacing the last digit of a(n) with the digit(s) of k^3. This is k(2).

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Magma

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A237342 For k in {2,3,...,9} define a sequence as follows: a(0)=0; for n>=0, a(n+1)=a(n)+1, unless a(n) ends in k, in which case a(n+1) is obtained by replacing the last digit of a(n) with the digit(s) of k^2. This is k(5).

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A237343 For k in {2,3,...,9} define a sequence as follows: a(0)=0; for n>=0, a(n+1)=a(n)+1, unless a(n) ends in k, in which case a(n+1) is obtained by replacing the last digit of a(n) with the digit(s) of k^2. This is k(6).

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Mathematica

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A237345 For k in {2,3,...,9} define a sequence as follows: a(0)=0; for n>=0, a(n+1)=a(n)+1, unless a(n) ends in k, in which case a(n+1) is obtained by replacing the last digit of a(n) with the digit(s) of k^2. This is k(8).

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