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.

User: Michael Joseph Halm

Michael Joseph Halm's wiki page.

Michael Joseph Halm has authored 71 sequences. Here are the ten most recent ones:

A126755 Braille numberdromes: numbers which read the same backwards and forwards in Braille.

Original entry on oeis.org

1, 2, 3, 7, 11, 22, 33, 46, 59, 64, 77, 80, 95, 111, 121, 131, 161, 171, 212, 222, 232, 262, 272, 313, 323, 333, 373, 416, 426, 436, 476, 519, 529, 539, 579, 614, 624, 634, 674, 717, 727, 737, 777, 810, 820, 830, 870, 915, 925, 935, 975
Offset: 1

Views

Author

Michael Joseph Halm, Apr 23 2007

Keywords

Comments

The pairs 4 and 6, 5 and 9 and 0 and 8 are mirror images of each other. When a Braille number is read backward (as a mirror-image) the number is usually not the same as the original. Those that are the same could be called by analogy with the ordinary numberdromes the Braille numberdromes. Those with "a double yolk", such as 1081, would be Braille numberddromes, by analogy with palinddromes.

Examples

			a(8) = 46 because in Braille 4 and 6 are mirror images of each other.

Crossrefs

Cf. A121018.

A101196 Position of n-th n after the decimal point in Pi.

Original entry on oeis.org

1, 16, 17, 36, 48, 72, 96, 74, 55, 854, 709, 1080, 1076, 1636, 1657, 1651, 889, 1674, 1227, 2039, 1486, 2372, 2690, 2288, 2033, 2282, 1785, 2703, 4155, 3102, 3584, 3767, 4325, 3808, 3551, 4081, 3785, 3229, 4464, 4884, 4127, 4228, 5336, 3961, 4242, 3633
Offset: 1

Views

Author

Michael Joseph Halm, Dec 12 2004

Keywords

Examples

			a(2) = 16 because the second occurrence of 2 in the digits of pi after its decimal point is at position 16, that is, after 141592653589793.

Crossrefs

Cf. A014777, A037000, A037001, A037002, A037003, A037004, A037005, A037006, A037007, A037008.

Extensions

Corrected and extended by Mark Hudson (mrmarkhudson(AT)hotmail.com), Dec 13 2004

A102045 Aronsonian sequence generated by the sentence, "H is the first, fifth, sixteenth, twenty-fifth, thirty-sixth, thirty-eighth, forty-seventh, ... letter in this sentence.".

Original entry on oeis.org

1, 5, 16, 25, 36, 38, 47, 49, 57, 59, 71, 81, 93, 103, 119, 133, 140, 148, 155, 171, 183, 189, 196, 200, 204, 229, 231, 235, 251, 255, 277, 287, 291, 298, 308, 315, 319, 335, 339, 347, 351, 363, 367, 384, 388, 396, 409, 417, 426, 430, 450, 466, 470, 490, 494
Offset: 1

Views

Author

Michael Joseph Halm, Feb 12 2005

Keywords

Comments

This version counts hyphens, A055508 does not.

Examples

			a(3) = 16 because the third H in "H is the first, fifth, ... letter in this sentence." is its 16th letter.

Crossrefs

Cf. A005224.

A102046 Smallest positive integer greater than a(n - 1) consistent with the condition that n is a member of the sequence if and only if a(n) is congruent to (n!)!.

Original entry on oeis.org

1, 1, 2, 6, 7, 8, 720, 721, 722, 723, 724, 726, 727, 728, 729, 780, 781, 782, 783, 784, 785, 786, 787, 789, 790, 791, 792, 793, 794, 795, 796, 797, 798, 799, 780, 781, 782, 783, 784, 785, 786, 787, 788, 789, 790, 791, 792, 793, 794, 795, 796, 797, 798, 799
Offset: 0

Views

Author

Michael Joseph Halm, Feb 12 2005

Keywords

Comments

The sequence is related to the fake even and fake odd sequences and also the factorial and double factorial sequences, so seems in the short run linear but in the long run exponential.

Examples

			a(6) = 720 because (3!)! = 6! = 720

Crossrefs

Cf. A080591, A080588, A000197, A000142.

Formula

a(a(n)) = (n!)!

Extensions

The definition does not match the data. How was this sequence generated? - N. J. A. Sloane, Feb 21 2021

A102069 Analogous to the oblong (promic or heteromecic) sequence formed but with reversal digits of factors multiplied.

Original entry on oeis.org

2, 6, 12, 20, 30, 42, 56, 72, 9, 11, 231, 651, 1271, 2091, 3111, 4331, 5751, 7371, 182, 24, 264, 704, 1344, 2184, 3224, 4464, 5904, 7544, 276, 39, 299, 759, 1419, 2279, 3339, 4599, 6059, 7719, 372, 56, 336, 816, 1496, 2376, 3456, 4736, 6216, 7896, 470, 75, 375
Offset: 1

Views

Author

Michael Joseph Halm, Feb 12 2005

Keywords

Crossrefs

Cf. A001129, A002378.

Programs

  • Mathematica
    r[n_]:=FromDigits[Reverse[IntegerDigits[n]]];Table[r[n]*r[n+1],{n,51}] (* James C. McMahon, Jan 07 2024 *)

Formula

a(n) = R(n)*R(n+1), where R(n) is the digital reversal of n.

A098129 Concatenate 1 once, 2 twice, 3 three times, up to n n times.

Original entry on oeis.org

1, 122, 122333, 1223334444, 122333444455555, 122333444455555666666, 1223334444555556666667777777, 122333444455555666666777777788888888, 122333444455555666666777777788888888999999999
Offset: 1

Views

Author

Michael Joseph Halm, Jan 04 2005

Keywords

Comments

a(n) is composite for all 2 <= n <= 1000. - David Cleaver, Mar 22 2023

Examples

			a(4) = 1223334444 because 1 concatenated once then concatenated with 2 twice and 3 three times and 4 four times gives 1223334444.

Links

Crossrefs

Cf. A000461, A300517, A361751 (number of decimal digits).

Programs

  • Maple
    a:= n-> parse(cat(seq(i$i, i=1..n))):
seq(a(n), n=1..12);  # Alois P. Heinz, Mar 07 2018
  • Mathematica
    nn = 12; a[0] = {}; Do[Set[a[n], Join[a[n - 1], Flatten@ ConstantArray[IntegerDigits[n], n]]], {n, nn}]; Array[FromDigits @* a, nn] (* Michael De Vlieger, Mar 29 2023 *)
  • PARI
    a(n) = {my(a=0,i,k);
  for(i=1,n, k = logint(i,10)+1;
    a = a*10^(i*k) + i*(10^(i*k)-1)/(10^k-1);
); return(a); } \\ David Cleaver, Mar 29 2023
  • Python
    def A098129(n): return int(''.join(str(j)*j for j in range(1,n+1))) # Chai Wah Wu, Mar 29 2023

Extensions

Offset and a(8) corrected by Seiichi Manyama, Mar 07 2018

A095762 Numbers whose name in English contains an "h".

Original entry on oeis.org

3, 8, 13, 18, 23, 28, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 43, 48, 53, 58, 63, 68, 73, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 93, 98, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124
Offset: 1

Views

Author

Michael Joseph Halm, Jul 10 2004

Keywords

Examples

			a(1) = 3 because "three" contains an "h", while 0, 1 and 2 do not

A095763 Numbers whose name in English contains an "i".

Original entry on oeis.org

5, 6, 8, 9, 13, 15, 16, 18, 19, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 45, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 75, 76, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99
Offset: 1

Views

Author

Michael Joseph Halm, Jul 10 2004

Keywords

Examples

			a(5) = 13 because "thirteen" contains an "i" and is the fifth integer to do so

Formula

A001477 \ A089589. [From R. J. Mathar, Apr 28 2009]

Extensions

Corrected by Rick L. Shepherd, Jul 10 2004

A095764 Numbers whose name in English contains an "l".

Original entry on oeis.org

11, 12, 111, 112, 211, 212, 311, 312, 411, 412, 511, 512, 611, 612, 711, 712, 811, 812, 911, 912, 1011, 1012, 1111, 1112, 1211, 1212, 1311, 1312, 1411, 1412, 1511, 1512, 1611, 1612, 1711, 1712, 1811, 1812, 1911, 1912, 2011, 2012, 2111, 2112, 2211, 2212
Offset: 1

Views

Author

Michael Joseph Halm, Jul 10 2004

Keywords

Examples

			a(3) = 111 because "one hundred eleven" contains a letter "l" and is only the third integer to do so

A095798 Numbers whose name in English contains a "v".

Original entry on oeis.org

5, 7, 11, 12, 17, 25, 27, 35, 37, 45, 47, 55, 57, 65, 67, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 85, 87, 95, 97, 105, 107, 111, 112, 117, 125, 127, 135, 137, 145, 147, 155, 157, 165, 167, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 185, 187, 195, 197, 205, 207
Offset: 1

Views

Author

Michael Joseph Halm, Jul 10 2004

Keywords

Comments

A008520 are numbers which contain an "e", A008540 an "f", A011538 a "g", A008536 an "n", A008519 an "o", A008538 an "s", A008522 a "t", A011534 a "u", A011532 a "w", A011536 an "x" and A008553 a "y"

Examples

			a(3) = 11 because "eleven" contains a "v" and it is the third number to do so (after "five" and "seven").

Crossrefs

Cf. A008520, A008540, A011538, A008536, A008519, A008538, A008522, A011534, A011532, A011536, A008553.

Extensions

Corrected by Rick L. Shepherd, Jul 10 2004

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

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