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

Author

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

Keywords

• base
• nonn

Comments

Phi = 1.61803398874989484820458683436... (see A001622).

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

Examples

			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 )
		

Crossrefs

Cf. A001622, A002113.

Cf. A138072, A138073.

Programs

Mathematica

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 *)