Felix Tubiana - cp's OEIS frontend

A178356 Fibonacci numbers whose successive digits decrease by 1.

0, 1, 2, 3, 5, 8, 21, 987

Offset: 1

Felix Tubiana, May 25 2010

Only need to consider the Fibonacci numbers less than 9876543210.

Join[{0,1,2,3,5,8},Select[Fibonacci[Range[250]],Union[Differences[ IntegerDigits[#]]]=={-1}&]] (* Harvey P. Dale, Sep 14 2011 *)

n=0;while((f=fibonacci(n))<=9876543210,if(is(f),print1(f", "));n++) \\ Charles R Greathouse IV, Sep 14 2011

{ A000045 } intersect { A138142 }. - Alois P. Heinz, Jul 05 2022

Definition clarified by Harvey P. Dale, Sep 14 2011

A178355 Fibonacci numbers with digits increased by 1.

Original entry on oeis.org

0, 1, 2, 3, 5, 8, 34, 89

Offset: 1

Felix Tubiana, May 25 2010

Fibonacci numbers such that they are either one-digit numbers or their digits all have differences of 1. - Harvey P. Dale, Jun 09 2022

Cf. A000045, A138141, A178356.

{ A000045 } intersect { A138141 }. - Alois P. Heinz, Jul 05 2022

Offset set to 1 by Alois P. Heinz, Jul 05 2022

A167231 Append three digits, each increasing by one modulo 10 from the last digit of the nonnegative integers. 0 -> 123, 1 -> 1234 2 -> 2345, ... , 9 -> 9012, 10 -> 10123, etc.

Original entry on oeis.org

123, 1234, 2345, 3456, 4567, 5678, 6789, 7890, 8901, 9012, 10123, 11234, 12345, 13456, 14567, 15678, 16789, 17890, 18901, 19012, 20123, 21234, 22345, 23456, 24567, 25678, 26789, 27890, 28901, 29012, 30123, 31234, 32345, 33456, 34567, 35678, 36789, 37890, 38901

Offset: 0

Felix Tubiana, Oct 30 2009

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,1,-1).

a:= n-> (d-> parse(cat(n, irem(d+i, 10)$i=1..3)))(irem(n, 10)):
seq(a(n), n=0..40);  # Alois P. Heinz, Jul 05 2022

def a(n): return int(str(n) + "".join(str((n%10+1+i)%10) for i in range(3)))
print([a(n) for n in range(39)]) # Michael S. Branicky, Jul 05 2022

a(n) = 1000n + O(1).

G.f.: (988*x^10 +111*x^9 +1011*x^8 +1101*x^7 +1111*x^6 +1111*x^5 +1111*x^4 +1111*x^3 +1111*x^2 +1111*x +123) / (x^11 -x^10 -x +1). - Alois P. Heinz, Jul 05 2022

More terms from Alois P. Heinz, Jul 05 2022

A167208 Append two digits, each increasing by one modulo 10 from the last digit of the positive integers. 0 -> 12 1 -> 123 2 -> 234 .. 9 -> 901 10 -> 1012.

Original entry on oeis.org

12, 123, 234, 345, 456, 567, 678, 789, 890, 901, 1012, 1123, 1234, 1345, 1456, 1567, 1678, 1789, 1890, 1901, 2012, 2123, 2234, 2345, 2456, 2567, 2678, 2789, 2890, 2901, 3012, 3123, 3234, 3345, 3456, 3567, 3678, 3789, 3890, 3901, 4012, 4123

Offset: 0

Felix Tubiana, Oct 30 2009

A138714 Add 1, modulo 10, to the decimal expansion of e, A001113.

Original entry on oeis.org

3, 8, 2, 9, 3, 9, 2, 9, 3, 9, 5, 6, 0, 1, 5, 6, 3, 4, 6, 4, 7, 1, 3, 9, 8, 5, 8, 2, 4, 6, 3, 7, 7, 3, 5, 0, 8, 8, 6, 8, 3, 5, 8, 1, 0, 4, 7, 0, 0, 0, 6, 0, 6, 8, 5, 0, 7, 7, 0, 7, 8, 7, 3, 8, 8, 3, 5, 1, 8, 7, 7, 4, 1, 4, 6, 4, 6, 5, 8, 6, 0, 5, 6, 8, 2, 4, 9, 3, 2, 8, 9, 6, 3, 6, 2, 7, 7, 5, 3, 8, 5, 3, 8, 5, 7

Offset: 1

Felix Tubiana, May 15 2008

			3.82939293956015634647139858...

Cf. A001113, A059833.

Mod[# + 1, 10] & /@ First@ RealDigits@ N[E, 105] (* Michael De Vlieger, Apr 01 2015 *)

[(floor((1+e*10^n))%10) for n in range(105)] # Danny Rorabaugh, Apr 01 2015

Offset set to 1 by Alois P. Heinz, Jul 05 2022

A101440 Replace each digit of n with 1 followed by n 0's: 0 -> 1, 1 -> 10, 2 -> 100, ..., 9 -> 1000000000, 10 -> 101, 11 -> 1010, 12 -> 10100, etc. Expanded number is then converted from binary to decimal: 0 -> 1 -> 1, 1 -> 10 -> 2, 2 -> 100 -> 4, 9 -> 1000000000 -> 512, 10 -> 101 -> 5, etc.

Original entry on oeis.org

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 5, 10, 20, 40, 80, 160, 320, 640, 1280, 2560, 9, 18, 36, 72, 144, 288, 576, 1152, 2304, 4608, 17, 34, 68, 136, 272, 544, 1088, 2176, 4352, 8704, 33, 66, 132, 264, 528, 1056, 2112, 4224, 8448, 16896, 65, 130, 260, 520, 1040

Offset: 0

Felix Tubiana, Jan 18 2005

			a(123) = 328 : 123 -> 101001000 -> 328.

A090915 Permutation of natural numbers arising from a square spiral.

Original entry on oeis.org

1, 8, 7, 6, 5, 4, 3, 2, 9, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 25, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 49, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, 58

Offset: 1

Felix Tubiana, Feb 26 2004

Write out the natural numbers in a square counterclockwise spiral:
.
  17--16--15--14--13
   |               |
  18   5---4---3  12
   |   |       |   |
  19   6   1---2  11
   |   |           |
  20   7---8---9--10
   |
  21--22--23--24--25
.
Now read off the numbers in a square clockwise spiral: 1 -> 8 -> 7 -> 6 -> 5 -> 4 -> 3 -> 2 -> 9 -> etc.

Eric M. Schmidt, Table of n, a(n) for n = 1..1000

Cf. A020703, A090861, A090925, A090928, A090929, A090930.

With[{x = Floor[(Floor[Sqrt[n-1]]+1)/2]}, Table[If[n==(2*x+1)^2, n, 8*x^2 -n+2], {n, 1, 75}]] (* G. C. Greubel, Feb 05 2019 *)

{s(n) = ((sqrtint(n-1)+1)/2)\1};
for(n=1,75, print1(if(n == (2*s(n)+1)^2, n, 8*s(n)^2-n+2), ", ")) \\ G. C. Greubel, Feb 05 2019

def a(n):
    x = (isqrt(n-1)+1)//2
    return n if n == (2*x+1)^2 else 8*x^2 + 2 - n
[a(n) for n in (1..75)] # Eric M. Schmidt, May 18 2016

Offset corrected by Eric M. Schmidt, May 18 2016

A090925 Permutation of natural numbers arising from a square spiral.

Original entry on oeis.org

1, 4, 5, 6, 7, 8, 9, 2, 3, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 10, 11, 12, 13, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 26, 27, 28, 29, 30, 31, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80

Offset: 1

Felix Tubiana, Feb 26 2004

Write out the natural numbers in a square counterclockwise spiral:
.
  17--16--15--14--13
   |               |
  18   5---4---3  12
   |   |       |   |
  19   6   1---2  11
   |   |           |
  20   7---8---9--10
   |
  21--22--23--24--25
.
Now read off the numbers in a square counterclockwise spiral: 1 -> 4 -> 5 -> 6 -> 7 -> 8 -> 9 -> 2 -> 3 -> 14 -> etc.

Eric M. Schmidt, Table of n, a(n) for n = 1..1000

Cf. A020703, A090861, A090915, A090928, A090929, A090930.

With[{x = Floor[(Floor[Sqrt[n-1]]+1)/2]}, Table[If[n+2*x <= (2*x+1)^2, n +2*x, n-6*x], {n, 1, 75}]] (* G. C. Greubel, Feb 05 2019 *)

{s(n) = ((sqrtint(n-1)+1)/2)\1};
for(n=1,75, print1(if(n+2*s(n) <= (2*s(n)+1)^2, n +2*s(n), n - 6*s(n)), ", ")) \\ G. C. Greubel, Feb 05 2019

def a(n):
    x = (isqrt(n-1)+1)//2
    return n + 2*x if n + 2*x <= (2*x+1)^2 else n - 6*x
[a(n) for n in (1..75)] # Eric M. Schmidt, May 18 2016

Offset corrected by Eric M. Schmidt, May 18 2016

A090929 Permutation of natural numbers arising from a square spiral.

Original entry on oeis.org

1, 8, 9, 2, 3, 4, 5, 6, 7, 22, 23, 24, 25, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 44, 45, 46, 47, 48, 49, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 74, 75, 76, 77, 78, 79, 80, 81, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64

Offset: 1

Felix Tubiana, Feb 26 2004

Write out the natural numbers in a square counterclockwise spiral:
.
  17--16--15--14--13
   |               |
  18   5---4---3  12
   |   |       |   |
  19   6   1---2  11
   |   |           |
  20   7---8---9--10
   |
  21--22--23--24--25
.
Now read off the numbers in a counterclockwise spiral: 1 -> 8 -> 9 -> 2 -> 3 -> 4 -> 5 -> 6 -> 7 -> 22 -> etc.

Eric M. Schmidt, Table of n, a(n) for n = 1..1000

Cf. A020703, A090861, A090915, A090925, A090928, A090930.

With[{x = Floor[(Floor[Sqrt[n-1]] +1)/2]}, Table[If[n +6*x <= (2*x+1)^2, n +6*x, n -2*x], {n, 1, 75}]] (* G. C. Greubel, Feb 05 2019 *)

{s(n) = ((sqrtint(n-1)+1)/2)\1};
for(n=1,75, print1(if(n+6*s(n) <= (2*s(n)+1)^2, n +6*s(n), n - 2*s(n)), ", ")) \\ G. C. Greubel, Feb 05 2019

def a(n):
    x = (isqrt(n-1)+1)//2
    return n + 6*x if n + 6*x <= (2*x+1)^2 else n - 2*x
[a(n) for n in (1..75)]
# Eric M. Schmidt, May 18 2016

Offset corrected by Eric M. Schmidt, May 18 2016

A090930 Permutation of natural numbers arising from a square spiral.

Original entry on oeis.org

1, 2, 9, 8, 7, 6, 5, 4, 3, 12, 11, 10, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 30, 29, 28, 27, 26, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 56, 55, 54, 53, 52, 51, 50, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66

Offset: 1

Felix Tubiana, Feb 26 2004

Write out the natural numbers in a square counterclockwise spiral:
.
  17--16--15--14--13
   |               |
  18   5---4---3  12
   |   |       |   |
  19   6   1---2  11
   |   |           |
  20   7---8---9--10
   |
  21--22--23--24--25
.
Now read off the numbers in a clockwise spiral: 1 -> 2 -> 9 -> 8 -> 7 -> 6 -> 5 -> 4 -> 3 -> 12 -> etc.

Eric M. Schmidt, Table of n, a(n) for n = 1..1000

Cf. A020703, A090861, A090915, A090925, A090928, A090929.

With[{x = Floor[(Floor[Sqrt[n-1]] +1)/2]}, Table[8*x^2 -n +2 +x*If[n <= 4*x^2 -2*x, -6, 2], {n, 1, 75}]] (* G. C. Greubel, Feb 05 2019 *)

{s(n) = ((sqrtint(n-1)+1)/2)\1};
for(n=1,75, print1(8*s(n)^2 -n +2 +s(n)*if(n <= 2*s(n)*(2*s(n)-1), -6, 2), ", ")) \\ G. C. Greubel, Feb 05 2019

def a(n):
    x = (isqrt(n-1)+1)//2
    return 8*x^2 + (-6 if n <= 4*x^2 - 2*x else 2)*x + 2 - n
[a(n) for n in (1..75)]
# Eric M. Schmidt, May 18 2016

Offset corrected by Eric M. Schmidt, May 18 2016

cp's OEIS Frontend

User: Felix Tubiana

A178356 Fibonacci numbers whose successive digits decrease by 1.

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A178355 Fibonacci numbers with digits increased by 1.

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A167231 Append three digits, each increasing by one modulo 10 from the last digit of the nonnegative integers. 0 -> 123, 1 -> 1234 2 -> 2345, ... , 9 -> 9012, 10 -> 10123, etc.

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A167208 Append two digits, each increasing by one modulo 10 from the last digit of the positive integers. 0 -> 12 1 -> 123 2 -> 234 .. 9 -> 901 10 -> 1012.

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Author

Keywords

A138714 Add 1, modulo 10, to the decimal expansion of e, A001113.

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Author

Keywords

Examples

Crossrefs

Programs

Mathematica

Sage

Extensions

A101440 Replace each digit of n with 1 followed by n 0's: 0 -> 1, 1 -> 10, 2 -> 100, ..., 9 -> 1000000000, 10 -> 101, 11 -> 1010, 12 -> 10100, etc. Expanded number is then converted from binary to decimal: 0 -> 1 -> 1, 1 -> 10 -> 2, 2 -> 100 -> 4, 9 -> 1000000000 -> 512, 10 -> 101 -> 5, etc.

Views

Author

Keywords

Examples

A090915 Permutation of natural numbers arising from a square spiral.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Sage

Extensions

A090925 Permutation of natural numbers arising from a square spiral.

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Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Sage

Extensions

A090929 Permutation of natural numbers arising from a square spiral.

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Author

Keywords

Comments

Links