cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 21-23 of 23 results.

A230833 Sum of the first n strobogrammatic numbers.

Original entry on oeis.org

0, 1, 9, 20, 89, 177, 273, 374, 485, 666, 1275, 1894, 2583, 3391, 4209, 5097, 6003, 6919, 7905, 8906, 10017, 11708, 13589, 15550, 21559, 27678, 34377, 41266, 48235, 56243, 64361, 73059, 81947, 90915, 99921, 109037
Offset: 1

Views

Author

G. L. Honaker, Jr., Oct 31 2013

Keywords

Examples

			a(10) = 666 because 0+1+8+11+69+88+96+101+111+181 = 666.

References

  • G. L. Honaker, Jr., Pentagrammic Decryption, unpublished.

Links

Crossrefs

Cf. partial sums of A000787.

A287092 Strobogrammatic nonpalindromic numbers.

Original entry on oeis.org

69, 96, 609, 619, 689, 906, 916, 986, 1691, 1961, 6009, 6119, 6699, 6889, 6969, 8698, 8968, 9006, 9116, 9696, 9886, 9966, 16091, 16191, 16891, 19061, 19161, 19861, 60009, 60109, 60809, 61019, 61119, 61819, 66099, 66199, 66899, 68089, 68189, 68889, 69069, 69169, 69869, 86098, 86198, 86898, 89068, 89168
Offset: 1

Views

Author

Ilya Gutkovskiy, May 19 2017

Keywords

Comments

Nonpalindromic numbers which are invariant under a 180-degree rotation.
Numbers that are the same upside down and containing digits 6, 9.
Intersection of A000787 and A029742.
Union of this sequence and A006072 gives A000787.

Crossrefs

Cf. A000787, A007597, A018848, A029742, A006072, A153806, A169731.

Programs

  • Mathematica
    fQ[n_] := Block[{s = {0, 1, 6, 8, 9}, id = IntegerDigits[n]}, If[ Union[ Join[s, id]] == s && (id /. {6 -> 9, 9 -> 6}) == Reverse[id], True, False]]; Select[ Range[0, 89168], fQ[ # ] && ! PalindromeQ[ # ] &]

A321702 Numbers that are still valid after a horizontal reflection on a calculator display.

Original entry on oeis.org

0, 1, 2, 3, 5, 8, 10, 11, 12, 13, 15, 18, 20, 21, 22, 23, 25, 28, 30, 31, 32, 33, 35, 38, 50, 51, 52, 53, 55, 58, 80, 81, 82, 83, 85, 88, 100, 101, 102, 103, 105, 108, 110, 111, 112, 113, 115, 118, 120, 121, 122, 123, 125, 128, 130, 131, 132, 133, 135, 138
Offset: 1

Views

Author

Kritsada Moomuang, Nov 17 2018

Keywords

Comments

Note that these numbers may not be unchanged after a horizontal reflection.
2 and 5 are taken as mirror images (as on calculator displays).
A007284 is a subsequence.
Also, numbers whose all digits are Fibonacci numbers. - Amiram Eldar, Feb 15 2024

Examples

			The sequence begins:
0, 1, 2, 3, 5, 8, 10, 11, 12, 13, ...;
0, 1, 5, 3, 2, 8, 10, 11, 15, 13, ...;
23 has its reflection as 53 in a horizontal mirror.
182 has its reflection as 185 in a horizontal mirror.

Links

Crossrefs

Cf. A000787, A007284, A018846.

Programs

  • Mathematica
    Select[Range[0, 140], Intersection[IntegerDigits[#], {4, 6, 7, 9}] == {} &] (* Amiram Eldar, Nov 17 2018 *)
  • PARI
    a(n, d=[0, 1, 2, 3, 5, 8]) = fromdigits(apply(k -> d[1+k], digits(n-1, #d))) \\ Rémy Sigrist, Nov 17 2018

Formula

Sum_{n>=2} 1/a(n) = 4.887249145579262560308470922947674796541485176473171687107616547235128170930... (calculated using Baillie and Schmelzer's kempnerSums.nb, see Links). - Amiram Eldar, Feb 15 2024
Previous Showing 21-23 of 23 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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