A256077 -id:A256077 - cp's OEIS frontend

A256290 Numbers which have only digits 4 and 5 in base 10.

4, 5, 44, 45, 54, 55, 444, 445, 454, 455, 544, 545, 554, 555, 4444, 4445, 4454, 4455, 4544, 4545, 4554, 4555, 5444, 5445, 5454, 5455, 5544, 5545, 5554, 5555, 44444, 44445, 44454, 44455, 44544, 44545, 44554, 44555, 45444, 45445, 45454, 45455, 45544

Offset: 1

M. F. Hasler, Mar 27 2015

Vincenzo Librandi, Table of n, a(n) for n = 1..8190
Index entries for 10-automatic sequences.

Cf. A007088 (digits 0 & 1), A007931 (digits 1 & 2), A032810 (digits 2 & 3), A032834 (digits 3 & 4), A256291 (digits 5 & 6), A256292 (digits 6 & 7), A256340 (digits 7 & 8), A256341 (digits 8 & 9).

[n: n in [1..60000] | Set(IntegerToSequence(n, 10)) subset {5, 4}];

[n: n in [1..100000] | Set(Intseq(n)) subset {4,5}]; // Vincenzo Librandi, Aug 19 2016

Flatten[Table[FromDigits[#,10]&/@Tuples[{4,5},n],{n,5}]]

A256290(n)=vector(#n=binary(n+1)[2..-1],i,10^(#n-i))*n~+10^#n\9*4

def A256290(n): return int(bin(n+1)[3:])+(10**((n+1).bit_length()-1)-1<<2)//9 # Chai Wah Wu, Jul 15 2023

a(n) = A007931(n) + A002277(A000523(n+1)) = A032834(n) + A256077(n) etc.

A256291 Numbers which have only digits 5 and 6 in base 10.

Original entry on oeis.org

5, 6, 55, 56, 65, 66, 555, 556, 565, 566, 655, 656, 665, 666, 5555, 5556, 5565, 5566, 5655, 5656, 5665, 5666, 6555, 6556, 6565, 6566, 6655, 6656, 6665, 6666, 55555, 55556, 55565, 55566, 55655, 55656, 55665, 55666, 56555, 56556

Offset: 1

M. F. Hasler, Mar 27 2015

Vincenzo Librandi, Table of n, a(n) for n = 1..8190
Index entries for 10-automatic sequences.

Cf. A007088 (digits 0 & 1), A007931 (digits 1 & 2), A032810 (digits 2 & 3), A032834 (digits 3 & 4), A256290 (digits 4 & 5), A256292 (digits 6 & 7), A256340 (digits 7 & 8), A256341 (digits 8 & 9).

[n: n in [1..60000] | Set(IntegerToSequence(n, 10)) subset {5, 6}];

[n: n in [1..100000] | Set(Intseq(n)) subset {5,6}]; // :Vincenzo Librandi_, Aug 19 2016

Flatten[Table[FromDigits[#,10]&/@Tuples[{5,6},n],{n,5}]]

A256291(n)=vector(#n=binary(n+1)[2..-1],i,10^(#n-i))*n~+10^#n\9*5

a(n) = A007931(n) + A002278(A000523(n+1)) = A256290(n) + A256077(n) etc.

A032834 Numbers with digits 3 and 4 only.

Original entry on oeis.org

3, 4, 33, 34, 43, 44, 333, 334, 343, 344, 433, 434, 443, 444, 3333, 3334, 3343, 3344, 3433, 3434, 3443, 3444, 4333, 4334, 4343, 4344, 4433, 4434, 4443, 4444, 33333, 33334, 33343, 33344, 33433, 33434, 33443, 33444, 34333, 34334

Offset: 1

Clark Kimberling

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for 10-automatic sequences.

Cf. A032829-A032833 (in other bases), A102659 (Lyndon words in this sequence), A007088 (digits 0 & 1), A007931 (digits 1 & 2), A032810 (digits 2 & 3), A256290 (digits 4 & 5), A256291 (digits 5 & 6), A256292 (digits 6 & 7), A256340 (digits 7 & 8), A256341 (digits 8 & 9).

[n: n in [1..35000] | Set(IntegerToSequence(n, 10)) subset {3, 4}]; // Vincenzo Librandi, May 30 2012

S[1]:= [3,4]:
for d from 2 to 5 do S[d]:= map(t -> (10*t+3,10*t+4), S[d-1]) od:
seq(op(S[d]),d=1..5); # Robert Israel, Apr 03 2017

Flatten[Table[FromDigits[#,10]&/@Tuples[{3,4},n],{n,5}]] (* Vincenzo Librandi, May 30 2012 *)

A032834(n)=vector(#n=binary(n+1)[2..-1],i,10^(#n-i))*n~+10^#n\3 \\ M. F. Hasler, Mar 27 2015

a(n) = A007931(n) + A002276(A000523(n+1)) = A032810(n) + A256077(n) etc. - M. F. Hasler, Mar 27 2015
From Robert Israel, Apr 03 2017: (Start)
a(2*n+1) = 10*a(n)+3.
a(2*n+2) = 10*a(n)+4.
G.f. g(x) satisfies g(x) = 10*(x+x^2)*g(x^2) + x*(3+4*x)/(1-x^2). (End)

Crossrefs added by M. F. Hasler, Mar 27 2015

Name corrected by Robert Israel, Apr 03 2017

A256292 Numbers which have only digits 6 and 7 in base 10.

Original entry on oeis.org

6, 7, 66, 67, 76, 77, 666, 667, 676, 677, 766, 767, 776, 777, 6666, 6667, 6676, 6677, 6766, 6767, 6776, 6777, 7666, 7667, 7676, 7677, 7766, 7767, 7776, 7777, 66666, 66667, 66676, 66677, 66766, 66767, 66776, 66777, 67666, 67667

Offset: 1

M. F. Hasler, Mar 27 2015

Vincenzo Librandi, Table of n, a(n) for n = 1..8190
Index entries for 10-automatic sequences.

Cf. A007088 (digits 0 & 1), A007931 (digits 1 & 2), A032810 (digits 2 & 3), A032834 (digits 3 & 4), A256290 (digits 4 & 5), A256291 (digits 5 & 6), A256340 (digits 7 & 8), A256341 (digits 8 & 9).

[n: n in [1..35000] | Set(IntegerToSequence(n, 10)) subset {7, 6}];

[n: n in [1..100000] | Set(Intseq(n)) subset {6,7}]; // Vincenzo Librandi, Aug 19 2016

Flatten[Table[FromDigits[#,10]&/@Tuples[{6,7},n],{n,5}]]

A256292(n)=vector(#n=binary(n+1)[2..-1],i,10^(#n-i))*n~+10^#n\9*6

a(n) = A007931(n) + A002279(A000523(n+1)) = A256291(n) + A256077(n) etc.

A256340 Numbers which have only digits 7 and 8 in base 10.

Original entry on oeis.org

7, 8, 77, 78, 87, 88, 777, 778, 787, 788, 877, 878, 887, 888, 7777, 7778, 7787, 7788, 7877, 7878, 7887, 7888, 8777, 8778, 8787, 8788, 8877, 8878, 8887, 8888, 77777, 77778, 77787, 77788, 77877, 77878, 77887, 77888, 78777, 78778, 78787, 78788, 78877, 78878

Offset: 1

M. F. Hasler, Mar 27 2015

Vincenzo Librandi, Table of n, a(n) for n = 1..8190
Index entries for 10-automatic sequences.

Cf. A007088 (digits 0 & 1), A007931 (digits 1 & 2), A032810 (digits 2 & 3), A032834 (digits 3 & 4), A256290 (digits 4 & 5), A256291 (digits 5 & 6), A256292 (digits 6 & 7), A256341 (digits 8 & 9).

[n: n in [1..35000] | Set(IntegerToSequence(n, 10)) subset {7, 8}];

[n: n in [1..100000] | Set(Intseq(n)) subset {7,8}]; // Vincenzo Librandi, Aug 19 2016

Flatten[Table[FromDigits[#,10]&/@Tuples[{7,8},n],{n,5}]]

A256340(n)=vector(#n=binary(n+1)[2..-1],i,10^(#n-i))*n~+10^#n\9*7

def a(n): return int(bin(n+1)[3:].replace('0', '7').replace('1', '8'))
print([a(n) for n in range(1, 45)]) # Michael S. Branicky, Jul 08 2021

a(n) = A007931(n) + A002280(A000523(n+1)) = A256292(n) + A256077(n) etc.

A256341 Numbers which have only digits 8 and 9 in base 10.

Original entry on oeis.org

8, 9, 88, 89, 98, 99, 888, 889, 898, 899, 988, 989, 998, 999, 8888, 8889, 8898, 8899, 8988, 8989, 8998, 8999, 9888, 9889, 9898, 9899, 9988, 9989, 9998, 9999, 88888, 88889, 88898, 88899, 88988, 88989, 88998, 88999, 89888, 89889

Offset: 1

M. F. Hasler, Mar 27 2015

Vincenzo Librandi, Table of n, a(n) for n = 1..8190
Index entries for 10-automatic sequences.

Cf. A007088 (digits 0 & 1), A007931 (digits 1 & 2), A032810 (digits 2 & 3), A032834 (digits 3 & 4), A256290 (digits 4 & 5) - A256292 (digits 6 & 7), A256340 (digits 7 & 8).

[n: n in [1..35000] | Set(IntegerToSequence(n, 10)) subset {8, 9}];

[n: n in [1..100000] | Set(Intseq(n)) subset {8,9}]; // Vincenzo Librandi, Aug 19 2016

Flatten[Table[FromDigits[#,10]&/@Tuples[{8,9},n],{n,5}]]

A256341(n)=vector(#n=binary(n+1)[2..-1],i,10^(#n-i))*n~+10^#n\9*8

def a(n): return int(bin(n+1)[3:].replace('0', '8').replace('1', '9'))
print([a(n) for n in range(1, 45)]) # Michael S. Branicky, Aug 09 2021

a(n) = A007931(n) + A002281(A000523(n+1)) = A256341(n) + A256077(n) etc.

cp's OEIS Frontend

A256290 Numbers which have only digits 4 and 5 in base 10.

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A256291 Numbers which have only digits 5 and 6 in base 10.

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Magma

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A032834 Numbers with digits 3 and 4 only.

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A256292 Numbers which have only digits 6 and 7 in base 10.

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Magma

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A256340 Numbers which have only digits 7 and 8 in base 10.

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Magma

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A256341 Numbers which have only digits 8 and 9 in base 10.

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Magma

Magma

Mathematica

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