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

Author

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

Keywords

• easy
• fini
• full
• nonn
• base

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.

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

Examples

			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
		

Links

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

Crossrefs

Cf. A002113, A134941.

Programs

Mathematica

ups = Flatten[Table[Range[i, j - 1], {i, 1, 9}, {j, i + 1, 10}], 1];afull = Sort[  Map[ToExpression@StringJoin@Map[ToString, #[[;; -2]] ~Join~ Reverse[#]] &, ups]];afull (* James C. McMahon, Apr 11 2025 *)

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

Formula

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