A134810 Giza numbers.

1, 2, 3, 4, 5, 6, 7, 8, 9, 121, 232, 343, 454, 565, 676, 787, 898, 12321, 23432, 34543, 45654, 56765, 67876, 78987, 1234321, 2345432, 3456543, 4567654, 5678765, 6789876, 123454321, 234565432, 345676543, 456787654, 567898765, 12345654321, 23456765432

Offset

1,2

Comments

For n > 9 the structure of digits represents the pyramids of Giza. Also the top of a mountain. The first digit is equal to the last digit. The first digits are in consecutive increasing order. The last digits are in consecutive decreasing order. The largest digit is the central digit. The number of digits is odd. This sequence has 45 terms. The final term is 12345678987654321. Giza numbers are mountain numbers A134941 and palindromes A002113.

A178333(a(n))*A136522(a(n)) = 1. - Reinhard Zumkeller, May 25 2010

There are 10 - k numbers with 2*k - 1 digits. - Omar E. Pol, Aug 04 2011

Links

Nathaniel Johnston, Table of n, a(n) for n = 1..45 (full sequence)

Example

Illustration using the final term of this sequence:
  . . . . . . . . 9 . . . . . . . .
  . . . . . . . 8 . 8 . . . . . . .
  . . . . . . 7 . . . 7 . . . . . .
  . . . . . 6 . . . . . 6 . . . . .
  . . . . 5 . . . . . . . 5 . . . .
  . . . 4 . . . . . . . . . 4 . . .
  . . 3 . . . . . . . . . . . 3 . .
  . 2 . . . . . . . . . . . . . 2 .
  1 . . . . . . . . . . . . . . . 1

Prog

(Python)
ups = [tuple(range(i, j)) for i in range(1, 10) for j in range(i+1, 11)]
afull = sorted(int("".join(map(str, u[:-1] + u[::-1]))) for u in ups)
print(afull) # Michael S. Branicky, Aug 02 2022

Crossrefs

Cf. A002113, A134941.

Sequence in context: A032567 A134853 A193407 * A173689 A004871 A059405

Adjacent sequences: A134807 A134808 A134809 * A134811 A134812 A134813

Keyword

easy,fini,full,nonn,base

Author

Omar E. Pol, Nov 25 2007, Nov 26 2007

Status

approved