A093783 -id:A093783 - cp's OEIS frontend

A002963 Number of chisel strokes required for Roman numerals for n.

1, 2, 3, 3, 2, 3, 4, 5, 3, 2, 3, 4, 5, 5, 4, 5, 6, 7, 5, 4, 5, 6, 7, 7, 6, 7, 8, 9, 7, 6, 7, 8, 9, 9, 8, 9, 10, 11, 9, 4, 5, 6, 7, 7, 6, 7, 8, 9, 7, 2, 3, 4, 5, 5, 4, 5, 6, 7, 5, 4, 5, 6, 7, 7, 6, 7, 8, 9, 7, 6, 7, 8, 9, 9, 8, 9, 10, 11, 9, 8, 9, 10, 11, 11, 10, 11, 12, 13, 11, 4, 5, 6, 7, 7, 6, 7, 8, 9, 7, 2, 3, 4

Offset: 1

N. J. A. Sloane

Chisel strokes for numerals: I,1; V,2; X,2; L,2; C ( = < ),2; D,3; M,4.
For more about Roman numerals, see A006968.
a(A002964(n)) = n. - Reinhard Zumkeller, Apr 14 2013

Nathaniel Johnston, Table of n, a(n) for n = 1..3999
Eric Weisstein's World of Mathematics, Roman Numerals
Wikipedia, Roman numerals

Cf. A119310.

Cf. A061493, A093783.

a002963 = ch 0 . a061493 where
     ch s 0 = s
     ch s x = ch (s + [0,1,2,2,2,2,3,4] !! d') x'
              where  (x',d) = divMod x 10; d' = fromInteger d
-- Reinhard Zumkeller, Apr 14 2013

with(StringTools): A002963 := proc(n) local r: r:=convert(n, roman): return add(parse(SubstituteAll( SubstituteAll( SubstituteAll( SubstituteAll( SubstituteAll( SubstituteAll( SubstituteAll(r[j], "I", "1"), "V", "2"), "X", "2"), "L", "2"), "C", "2"), "D", "3"), "M", "4")), j=1..length(r)): end: seq(A002963(n), n=1..102); # Nathaniel Johnston, May 18 2011

a[n_] := Characters[ IntegerString[n, "Roman"]] /. {"I" -> 1, "V" -> 2, "X" -> 2, "L" -> 2, "C" -> 2, "D" -> 3, "M" -> 4} // Total; Table[a[n], {n, 1, 102}] (* Jean-François Alcover, Sep 10 2013 *)

{A002963(n, c=[1000, 4, 900, 6, 500, 3, 400, 5, 100, 2, 90, 4, 50, 2, 40, 4, 10, 2, 9, 3, 5, 2, 4, 3, 1, 1], s=0)= forstep(i=1, #c, 2, while(n>=c[i], n-=c[i]; s+=c[i+1])); s} \\ M. F. Hasler, Jul 27 2016

a002963 = lambda n: sum((d+1-(d==2))*(i%5)+(d+2-(d==1))*(i>4) if (i+1)%5 else 3+d+(d==2)*(i==9) for d,i in enumerate(map(int,str(n)[::-1])))
# Nicholas Stefan Georgescu, Feb 27 2023

More terms from David W. Wilson

Data double-checked by M. F. Hasler, Jul 27 2016

A094153 a(n) is least prime p such that 7 is the n-th term in the Euclid-Mullin sequence starting at p, or 0 if no such prime p exists.

Original entry on oeis.org

7, 0, 2, 43, 11, 13, 31, 149, 347, 23, 439, 223, 461, 173, 5, 71, 197, 1153, 191, 307, 1657, 971, 9473, 19, 2399, 1607, 6781, 89, 9187, 281, 23623, 15077, 25579, 17203

Offset: 1

Labos Elemer, May 05 2004

The sequence is not monotonic. Compare to A093882.

Next term exceeds 50000. - Sean A. Irvine, Jan 12 2012

			a(5)=11 because p=7 first arises in EM at position 5, which is initiated with 11: {11,2,23,3,7,10627,433}; see A051309.

Cf. A000945, A051308-A051334, A056756, A093777-A093783.

Definition clarified, terms corrected and extended by Sean A. Irvine, Apr 15 2011
More terms from Sean A. Irvine, May 22 2011
25579 and 17203 from Sean A. Irvine, Jan 11 2012

A105247 Product of digits of Roman Numerals.

Original entry on oeis.org

1, 1, 1, 5, 5, 5, 5, 5, 10, 10, 10, 10, 10, 50, 50, 50, 50, 50, 100, 100, 100, 100, 100, 500, 500, 500, 500, 500, 1000, 1000, 1000, 1000, 1000, 5000, 5000, 5000, 5000, 5000, 10000, 500, 500, 500, 500, 2500, 2500, 2500, 2500, 2500, 5000, 50, 50, 50, 50, 250

Offset: 1

Jonathan Vos Post, Apr 14 2005

New Roman Numerals A006968 (i.e., 4 = IV, not IIII). Related to sum of digits of n in Roman numeral representation A093783.

			a(3) = 1 because 3 = "III" and I*I*I = I = 1.
a(4) = 5 because 4 = "IV" and I*V = V = 5.
a(9) = 10 because 9 = "IX" and I*X = X = 10.
a(14) = 50 because 14 = "XIV" and X*I*V = L = 50.
a(19) = 100 because 19 = "XIX" and X*I*X = C = 100.
a(24) = 500 because 24 = "XXIV" and X*X*I*V = D = 500.
a(29) = 1000 because 29 = "XXIX" and X*X*I*X = M = 1000.
a(34) = 5000 because 34 = "XXXIV" and X*X*X*I*V = 5000.
a(39) = 10000 because 39 = "XXXIX" and X*X*X*I*X = myriad = 10000.
a(40) = 500 because 40 = "XL" and X*L = D = 500.
a(44) = 2500 because 44 = "XLIV" and X*L*I*V = MMD = 2500.
a(49) = 5000 because 49 = "XLIX" and X*L*I*X = 5000.
a(50) = 50 because 50 = L.

Nathaniel Johnston, Table of n, a(n) for n = 1..3999
Gerard Schildberger and Frank Ellermann, The numbers from 1 to 3999 expressed as Roman numerals.

Cf. A006968, A093783.

with(StringTools): A105247 := proc(n) local r: r:=convert(n, roman): return mul(parse(SubstituteAll( SubstituteAll( SubstituteAll( SubstituteAll( SubstituteAll( SubstituteAll( SubstituteAll(r[j], "I", "1"), "V", "5"), "X", "10"), "L", "50"), "C", "100"), "D", "500"), "M", "1000")),j=1..length(r)): end: seq(A105247(n),n=1..54); # Nathaniel Johnston, May 18 2011

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A002963 Number of chisel strokes required for Roman numerals for n.

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A094153 a(n) is least prime p such that 7 is the n-th term in the Euclid-Mullin sequence starting at p, or 0 if no such prime p exists.

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A105247 Product of digits of Roman Numerals.

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Maple