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 11-16 of 16 results.

A133194 Numbers requiring a prime number of chisel strokes for their representation in Roman numerals.

Original entry on oeis.org

2, 3, 4, 5, 6, 8, 9, 10, 11, 13, 14, 16, 18, 19, 21, 23, 24, 26, 29, 31, 38, 41, 43, 44, 46, 49, 50, 51, 53, 54, 56, 58, 59, 61, 63, 64, 66, 69, 71, 78, 83, 84, 86, 88, 89, 91, 93, 94, 96, 99, 100, 101, 103, 104, 106, 108, 109, 111, 113, 114, 116, 119, 121
Offset: 1

Views

Author

Jonathan Vos Post, Oct 09 2007

Keywords

Comments

Finite if one excludes multiple strokes chiseled over the letter, each meaning multiplication by 1000. The subsequence "primes requiring a prime number of chisel strokes for its representation in Roman numerals" begins 2, 3, 5, 11, 13, 19, 23, 29, 31, 41, 43, 53, 59, 61, 71, 83, 89, 101, 103. This sequence uses the definition of strokes given in A002963, not A118098.

Examples

			a(1) = 2 because II requires 2 strokes (neglecting serifs).
a(44) = 88 because LXXXVIII requires 13 strokes.

Links

Crossrefs

Cf. A000040, A002963, A105269, A131480.

Formula

A002963(a(n)) is in A000040.

A164058 Number of curves in n-th letter of capitalized English alphabet (A being first).

Original entry on oeis.org

0, 2, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0
Offset: 1

Views

Author

Jonathan Vos Post, Aug 08 2009

Keywords

Comments

"Curve" as was excluded from sums in A163828. Curves are classified as: circle as occurs in {O, Q}, semicircle as in {B (twice), C, D, G, J, P, R, U}, and other {S}. We do not consider "S" as two semicircles, nor make various approximations of curves as sequences of line segments (as in A002963). In conjunction with A163828, we may sum the number of curves and straight line segments in an English magiscule (capital) letter, and thus derive an integer total of the number of straight and curved segments in the spelled-out English name of any nonnegative integer.

Examples

			a(2) = 2 because of the two semicircles in the 2nd letter, B. a(k) = 0 for k = {the letters occurring in A163670} = {A, E, F, H, I, K, L, M, N, T, V, W, X, Y, Z}.

Crossrefs

Cf. A002963, A005589, A163670, A163828.

A164059 Number of straight plus curved segments in the capitalized English name of n.

Original entry on oeis.org

11, 8, 7, 16, 8, 10, 4, 14, 13, 11, 9, 19, 18, 22, 21, 20, 17, 27, 24, 24, 18, 26, 25, 34, 26, 28, 22, 32, 31, 29, 14, 22, 21, 30, 22, 24, 18, 28, 27, 25, 12, 20, 19, 28, 20, 22, 16, 26, 25, 23, 12, 20, 19, 28, 20, 22, 16, 26, 25, 23, 9, 17, 16, 25, 17, 19, 13, 23, 22, 20, 19
Offset: 0

Views

Author

Jonathan Vos Post, Aug 08 2009

Keywords

Comments

Number of straight plus curved segments in all letters of the name of n, excluding hyphens.

Examples

			a(0) = 11 because ZERO has (letter by letter) 3+4+2+0 = 9 straight line segments (chisel strokes) and 0+0+1+1 = 2 curves as in A164058, with 9 + 2 = 11.
a(1) = 8 because of 1 curve in O, plus 3 chisel strokes in N and 4 chisel strokes in E, summing to 8 segments (straight or curved) in ONE.

Crossrefs

Cf. A002963, A005589, A163670, A163828, A164058.

Programs

  • Maple
    names :=["zero", "one", "two", "three", "four", "five", "six", "seven", "eight",
"nine", "ten", "eleven", "twelve", "thirteen", "fourteen", "fifteen", "sixteen",
"seventeen", "eighteen", "nineteen", "twenty", "twentyone", "twentytwo", "twentythree",
"twentyfour", "twentyfive", "twentysix", "twentyseven", "twentyeight", "twentynine", "thirty",
"thirtyone", "thirtytwo", "thirtythree", "thirtyfour", "thirtyfive", "thirtysix",
"thirtyseven", "thirtyeight", "thirtynine", "forty", "fortyone", "fortytwo",
"fortythree", "fortyfour", "fortyfive", "fortysix", "fortyseven", "fortyeight",
"fortynine", "fifty", "fiftyone", "fiftytwo", "fiftythree", "fiftyfour",
"fiftyfive", "fiftysix", "fiftyseven", "fiftyeight", "fiftynine", "sixty",
"sixtyone", "sixtytwo", "sixtythree", "sixtyfour", "sixtyfive", "sixtysix",
"sixtyseven", "sixtyeight", "sixtynine", "seventy", "seventyone", "seventytwo",
"seventythree", "seventyfour", "seventyfive", "seventysix", "seventyseven",
"seventyeight", "seventynine", "eighty", "eightyone", "eightytwo", "eightythree",
"eightyfour", "eightyfive", "eightysix", "eightyseven", "eightyeight", "eightynine",
"ninety", "ninetyone", "ninetytwo", "ninetythree", "ninetyfour", "ninetyfive",
"ninetysix", "ninetyseven", "ninetyeight", "ninetynine", "onehundred"] :
cstrok := [ 3, 1, 0, 1, 4, 3, 2, 3, 1, 1, 3, 2, 4, 3, 0, 1, 1, 2, 0, 2, 0, 2, 4, 2, 3, 3 ] ;
A164058 := [ 0, 2, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0] ;
A164059 := proc(n) global names, cstrok, A164058; local a,idx ; a := 0 ; for c in StringTools[Explode]( names[n+1]) do idx := StringTools[Ord](c)-96 ; a := a+ cstrok[idx]+A164058[idx] ; od: a ; end:
seq(A164059(n),n=0..70) ; # R. J. Mathar, Sep 29 2009

Formula

a(n) = A163828(n) + (number of curves in the letters of the English name of n as in A164058).
a(n) = A163828(n) for n in A163670.

Extensions

More terms from R. J. Mathar, Sep 29 2009

A133192 Numbers that require exactly five chisel strokes when written in Roman numerals.

Original entry on oeis.org

8, 13, 14, 16, 19, 21, 41, 53, 54, 56, 59, 61, 91, 103, 104, 106, 109, 111, 151, 201, 400, 502, 505, 510, 550, 600, 1001, 5002, 5005, 5010, 5050, 5100, 10002, 10005, 10010, 10050, 10100, 50002, 50005, 50010, 50050, 50100, 100002, 100005, 100010, 100050, 100100, 500001, 1000000
Offset: 1

Views

Author

Jonathan Vos Post, Oct 09 2007

Keywords

Examples

			Chisel strokes for numerals: I,1; V,2; X,2; L,2; C ( = < ),2; D,3; M,4; 5000 is V with a line over it, 3; 10000 is X with a line over it, 3; 50000 is L with a line over it, 3; 100000 is L with a line over it, 3; 500000 is D with a line over it, 4; 1000000 is M with a line over it, 5. Numerals with two horizontal strokes over them were not common in historical Rome. A002964 has a different evaluation of the strokes of C, as does A118098.

Crossrefs

Cf. A002963, A002964, A118098.

Formula

Numbers n such that A002963(n) = 5.

A164052 Numbers divisible by the number of chisel strokes in their English name (capitalized, excluding hyphens, excluding curves).

Original entry on oeis.org

6, 16, 29, 40, 66, 72, 93, 104, 126, 138, 144, 180, 200, 216, 240, 264, 280, 462, 468, 490, 492, 495, 630, 665, 675, 704, 720, 740, 756, 765, 795, 861, 900, 945, 988, 1078, 1281, 1320, 1386, 1410, 1428, 1440, 1450, 1518, 1566, 1586, 1620, 1736, 1800, 1825
Offset: 1

Views

Author

Jonathan Vos Post, Aug 08 2009

Keywords

Comments

For k = 1, 2, 3, 5, 16, 29, k divides A163828(k). "Capitalized" means all-caps, magiscule, in a sans serif font.

Examples

			a(1) = 16 and a(2) = 29 are fixed points of A163828. a(3) = 40 because "FORTY" has 10 chisel strokes, and 4*10 = 40.

Crossrefs

Cf. A002963, A005589, A163670, A163828.

Formula

{k such that A163828(k) | k}.

Extensions

a(1) = 6 inserted and terms after a(5) from Nathaniel Johnston, May 08 2011

A238365 Number of dots needed to express n as a Roman numeral in Braille.

Original entry on oeis.org

2, 4, 6, 6, 4, 6, 8, 10, 6, 4, 6, 8, 10, 10, 8, 10, 12, 14, 10, 8, 10, 12, 14, 14, 12, 14, 16, 18, 14, 12, 14, 16, 18, 18, 16, 18, 20, 22, 18, 7, 9, 11, 13, 13, 11, 13, 15, 17, 13, 3, 5, 7, 9, 9, 7, 9, 11, 13, 9, 7, 9, 11, 13, 13, 11, 13, 15, 17, 13, 11, 13, 15
Offset: 1

Views

Author

Arkadiusz Wesolowski, Feb 25 2014

Keywords

Examples

			VII in Braille (with the "Roman num" character):
  o  o      o    o
     o    o    o
  o  o o
Therefore a(7) = 10 - 2 = 8.

Links

Crossrefs

Cf. also A002963, A048181, A030166, A072283, A079399, A121018, A220090.

Programs

  • PARI
    a=[2, 4, 6, 6, 4, 6, 8, 10, 6, 0]; b=[0, 4, 8, 12, 7, 3, 7, 11, 15, 6]; for(n=1, 72, if(n<100, print1(a[lift(Mod(n-1, 10))+1]+b[floor(n/10)+1], ", "), break));
  • PARI
    /* The program works for n < 40 */
b=0; for(n=1, 39, if(Mod(n, 10)==0, b=b+4); m=lift(Mod(n, 10)); a=2*m-6; if(Mod(m, 5)==4, d=abs(a-7)+b+1, if(m<4, d=a+b+6, d=a+b)); print1(d, ", "));
Previous Showing 11-16 of 16 results.

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