A135699 -id:A135699

Search: a135699 -id:a135699

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A138073

Triangle read by rows: row n lists the digits of A135699(n), the palindromic number with odd number of digits formed from the reflected decimal expansion of golden ratio phi.

+20
4

1, 1, 6, 1, 1, 6, 1, 6, 1, 1, 6, 1, 8, 1, 6, 1, 1, 6, 1, 8, 0, 8, 1, 6, 1, 1, 6, 1, 8, 0, 3, 0, 8, 1, 6, 1, 1, 6, 1, 8, 0, 3, 3, 3, 0, 8, 1, 6, 1, 1, 6, 1, 8, 0, 3, 3, 9, 3, 3, 0, 8, 1, 6, 1, 1, 6, 1, 8, 0, 3, 3, 9, 8, 9, 3, 3, 0, 8, 1, 6, 1

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

COMMENTS

Also, successive digits of the terms of A135699.

LINKS

G. C. Greubel, Table of n, a(n) for the first 50 rows

EXAMPLE

Triangle begins:

.............. 1

........... 1, 6, 1

........ 1, 6, 1, 6, 1

..... 1, 6, 1, 8, 1, 6, 1

.. 1, 6, 1, 8, 0, 8, 1, 6, 1

MATHEMATICA

nn=10; With[{phi=RealDigits[GoldenRatio, 10, nn+1][[1]]}, Flatten[ Table[ Join[Take[phi, n], Take[phi, {n+1}], Reverse[Take[phi, n]]], {n, 0, nn}]]] (* Harvey P. Dale, May 08 2012 *)

CROSSREFS

Decimal expansion of phi: A001622. Cf. A135699, A135700, A138072.

KEYWORD

easy,nonn,tabf,base

AUTHOR

Omar E. Pol, Mar 03 2008

STATUS

approved

A011551

Decimal expansion of phi truncated to n places.

+10
7

1, 16, 161, 1618, 16180, 161803, 1618033, 16180339, 161803398, 1618033988, 16180339887, 161803398874, 1618033988749, 16180339887498, 161803398874989, 1618033988749894, 16180339887498948, 161803398874989484, 1618033988749894848, 16180339887498948482

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

MATHEMATICA

With[{phi=RealDigits[GoldenRatio, 10, 50][[1]]}, Table[FromDigits[ Take[ phi, n]], {n, 20}]] (* Harvey P. Dale, Feb 03 2012 *)

PROG

(PARI) my(phi=quadgen(5)); a(n) = floor(phi*10^n); \\ Kevin Ryde, Jun 05 2021

CROSSREFS

Cf. A001622 (phi), A138116 (triangle of digits), A195607 (fraction), A276198 (next prime).

Palindromes: A135699, A135700.

KEYWORD

nonn,base

AUTHOR

N. J. A. Sloane.

STATUS

approved

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.

+10
4

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

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,5

COMMENTS

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

LINKS

Table of n, a(n) for n=1..78.

EXAMPLE

Triangle begins:

...... 1

..... 1,1

.... 1,6,1

... 1,6,6,1

.. 1,6,1,6,1

CROSSREFS

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

KEYWORD

easy,nonn,tabl,base

AUTHOR

Omar E. Pol, Mar 03 2008

STATUS

approved

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