A138073 -id:A138073 - cp's OEIS frontend

A135700 Palindromes formed from the reflected decimal expansion of golden ratio phi.

1, 11, 161, 1661, 16161, 161161, 1618161, 16188161, 161808161, 1618008161, 16180308161, 161803308161, 1618033308161, 16180333308161, 161803393308161, 1618033993308161, 16180339893308161, 161803398893308161, 1618033988893308161, 16180339888893308161, 161803398878893308161

Offset: 1

Omar E. Pol, Mar 01 2008, Mar 28 2008

Phi = 1.61803398874989484820458683436... (see A001622).

The number of digits of a(n) is equal to n.

			n ... Successive digits of a(n)
1 ............ ( 1 )
2 ........... ( 1 1 )
3 .......... ( 1 6 1 )
4 ......... ( 1 6 6 1 )
5 ........ ( 1 6 1 6 1 )
6 ....... ( 1 6 1 1 6 1 )
7 ...... ( 1 6 1 8 1 6 1 )
8 ..... ( 1 6 1 8 8 1 6 1 )
9 .... ( 1 6 1 8 0 8 1 6 1 )
10 .. ( 1 6 1 8 0 0 8 1 6 1 )

Cf. A001622, A002113.

Cf. A138072, A138073.

gr=RealDigits[GoldenRatio, 10, 50][[1]]; (* increase for n>100 *)a[n_]:=FromDigits[Join[Take[gr, Ceiling[n/2]], Reverse[Take[gr, n-Ceiling[n/2]]]]]; Array[a, 20] (* James C. McMahon, Apr 29 2025 *)

A138072 Triangle read by rows: row n lists the digits of A135700(n), the palindromic number formed from the reflected decimal expansion of golden ratio phi.

Original entry on oeis.org

1, 1, 1, 1, 6, 1, 1, 6, 6, 1, 1, 6, 1, 6, 1, 1, 6, 1, 1, 6, 1, 1, 6, 1, 8, 1, 6, 1, 1, 6, 1, 8, 8, 1, 6, 1, 1, 6, 1, 8, 0, 8, 1, 6, 1, 1, 6, 1, 8, 0, 0, 8, 1, 6, 1, 1, 6, 1, 8, 0, 3, 0, 8, 1, 6, 1, 1, 6, 1, 8, 0, 3, 3, 0, 8, 1, 6, 1

Offset: 1

Omar E. Pol, Mar 03 2008

Also, successive digits of the numbers A135700(n).

			Triangle begins:
...... 1
..... 1,1
.... 1,6,1
... 1,6,6,1
.. 1,6,1,6,1

Decimal expansion of phi: A001622. Cf. A135699, A135700, A135696, A138073.

A138116 Triangle read by rows: row n lists the first n digits of the decimal expansion of golden ratio phi.

Original entry on oeis.org

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

Offset: 1

Omar E. Pol, Mar 14 2008

Also, successive digits of A011551.

			Triangle begins:
      1
     1,6
    1,6,1
   1,6,1,8
  1,6,1,8,0

Cf. A001622 (phi), A011551, A138072, A138073, A175834 (polynomial roots).

s={};Do[AppendTo[s,RealDigits[GoldenRatio,10,n][[1]]],{n,12}];s//Flatten (* James C. McMahon, Jun 05 2025 *)

cp's OEIS Frontend

A135700 Palindromes formed from the reflected decimal expansion of golden ratio phi.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

A138072 Triangle read by rows: row n lists the digits of A135700(n), the palindromic number formed from the reflected decimal expansion of golden ratio phi.

Views

Author

Keywords

Comments

Examples

Crossrefs

A138116 Triangle read by rows: row n lists the first n digits of the decimal expansion of golden ratio phi.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica