A052360 -id:A052360 - cp's OEIS frontend

A266851 The last letter of the English name of a(n) equals the a(n)-th letter of the concatenation of all the terms spelled out in English.

4, 2, 10, 8, 9, 16, 18, 25, 33, 40, 50, 55, 60, 70, 78, 81, 83, 98, 99, 119, 125, 133, 139, 153, 155, 157, 168, 188, 201, 215, 217, 221, 241, 277, 293, 331, 337, 365, 367, 368, 378, 394, 395, 402, 410, 419, 423, 425, 434, 435, 437, 448, 451, 467, 473, 479, 484, 494, 495, 500, 506, 512, 523, 528, 531, 533, 539, 544, 545, 561

Offset: 1

Eric Angelini, Hans Havermann and M. F. Hasler, Jan 04 2016

			a(2)=2, so that the last letter of two, o, is the 2nd letter of a(1)=4, four.

A266851(n,show=1,a=4,u=0,s=[],E=k->select(t->t>"@",Vec(English(k))))={for(n=2,n,show&&print1(a",");s=concat(s,E(a));u+=1<A052360. Optional args allow imposing special constraints or use of another language.

A082655 Number of distinct letters needed to spell English names of numbers 1 through n.

Original entry on oeis.org

3, 5, 7, 9, 11, 13, 13, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16

Offset: 1

Peter F. Klammer (pklammer(AT)acm.org), May 17 2003

Late increases are at twentY, hunDred, thousAnd, Million, Billion, Quadrillion, sePtillion, oCtillion.

Only J and K are never used for English number names. Z is used only for zero.

			"One" has three letters, "two" brings two new letters (t w), "three" brings two more (h r)...

Cf. A005589, A052360, A052362, A052363.

Edited by Don Reble, Nov 03 2003

More terms from Jinyuan Wang, Apr 07 2020

A118622 Numbers whose English names are 5 letters long.

Original entry on oeis.org

3, 7, 8, 40, 50, 60

Offset: 1

Dylan Nicholson (wizofaus(AT)hotmail.com), May 08 2006

A005589(a(n)) = 5 and A052360(a(n)) = 5. - Michel Marcus, Aug 18 2013

Subsequence of A052194.

Erroneous term 5 (that has 4 letters) removed by Michel Marcus, Aug 18 2013

A132204 Sum of the numerical equivalents for the 23 Latin letters, according to Tartaglia, of the letters in the English name of n, excluding spaces and hyphens.

Original entry on oeis.org

2341, 351, 0, 940, 0, 296, 81, 665, 1011, 431, 500

Offset: 0

Jonathan Vos Post, Nov 19 2007

Which are the fixed points n such that a(n) = n? Which n have prime a(n)? What are the equivalence classes of integers that have the same a(n)? Which n divide a(n)? Which n have a(n) that can be read as binary, as with a(8) = 1011? What is the sequence of n such that a(n) = 0 (i.e. the English name on n contains a J, U, or W)?

This sequence seems unnatural, since English uses three letters that were not in the Latin alphabet (W, U, J). A better sequence would first write the names of the numbers in Latin (cf. A132984) and then sum the values of the letters. - N. J. A. Sloane, Nov 30 2007

			a(0) = A132475(ZERO) = A132475(Z)+A132475(E)+A132475(R)+A132475(O) = 2000 + 250 + 80 + 11 = 2341.
a(1) = A132475(ONE) = A132475(O)+A132475(N)+A132475(E) = 11 + 90 + 250 = 351.
a(2) = 0 because "TWO" contains a "W" which is not one of Tartaglia's letters.
a(3) = A132475(THREE) = 160 + 200 + 80 + 250 + 250 = 940.
a(4) = 0 because "FOUR" contains a "U" which is not one of Tartaglia's letters.
a(5) = A132475(FIVE) = 40 + 1 + 5 + 250 = 296.
a(6) = A132475(SIX) = 70 + 1 + 10 = 81.
a(7) = A132475(SEVEN) = 70 + 250 + 5 + 250 + 90 = 665.
a(8) = A132475(EIGHT) = 250 + 1 + 400 + 200 + 160 = 1011.
a(9) = A132475(NINE) = 90 + 1 + 90 + 250 = 431.
a(10) = A132475(TEN) = 160 + 250 + 90 = 500 = A132475(Q).

Cf. A005589, A052360, A052362-A052363, A134629, A132475.

A175725 Number of characters in the Polish name of n, including spaces and hyphens.

Original entry on oeis.org

4, 5, 3, 4, 6, 4, 5, 6, 5, 8, 8, 10, 9, 10, 11, 10, 10, 12, 11, 14, 11, 17, 15, 16, 18, 16, 17, 18, 17, 20, 11, 17, 15, 16, 18, 16, 17, 18, 17, 20, 12, 18, 16, 17, 19, 17, 18, 19, 18, 21, 12, 18, 16, 17, 19, 17, 18, 19, 18, 21, 13, 19, 17, 18, 20, 18, 19, 20, 19, 22, 14, 20, 18

Offset: 0

Artur Jasinski, Aug 18 2010

Cf. A005589, A052360, A008962

t = {"zero", "jeden", "dwa", "trzy", "cztery", "piec", "szesc", "siedem", "osiem", "dziewiec", "dziesiec", "jedenascie", "dwanascie", "trzynascie", "czternascie", "pietnascie", "szesnascie", "siedemnascie", "osiemnascie", "dziewietnascie", "dwadziescia", "dwadziescia jeden", "dwadziescia dwa", "dwadziescia trzy", "dwadziescia cztery", "dwadziescia piec", "dwadziescia szesc", "dwadziescia siedem", "dwadziescia osiem", "dwadziescia dziewiec", "trzydziesci", "trzydziesci jeden", "trzydziesci dwa", "trzydziesci trzy", "trzydziesci cztery", "trzydziesci piec", "trzydziesci szesc", "trzydziesci siedem", "trzydziesci osiem",
"trzydziesci dziewiec", "czterdziesci", "czterdziesci jeden", "czterdziesci dwa", "czterdziesci trzy", "czterdziesci cztery", "czterdziesci piec", "czterdziesci szesc", "czterdziesci siedem", "czterdziesci osiem", "czterdziesci dziewiec", "piecdziesiat", "piecdziesiat jeden", "piecdziesiat dwa", "piecdziesiat trzy", "piecdziesiat cztery", "piecdziesiat piec", "piecdziesiat szesc", "piecdziesiat siedem", "piecdziesiat osiem", "piecdziesiat dziewiec", "szescdziesiat", "szescdziesiat jeden", "szescdziesiat dwa", "szescdziesiat trzy", "szescdziesiat cztery", "szescdziesiat piec", "szescdziesiat szesc", "szescdziesiat siedem", "szescdziesiat osiem", "szescdziesiat dziewiec", "siedemdziesiat", "siedemdziesiat jeden", "siedemdziesiat dwa", "siedemdziesiat trzy", "siedemdziesiat cztery", "siedemdziesiat piec", "siedemdziesiat szesc", "siedemdziesiat siedem", "siedemdziesiat osiem", "siedemdziesiat dziewiec", "osiemdziesiat",
"osiemdziesiat jeden", "osiemdziesiat dwa", "osiemdziesiat trzy", "osiemdziesiat cztery", "osiemdziesiat piec", "osiemdziesiat szesc", "osiemdziesiat siedem", "osiemdziesiat osiem", "osiemdziesiat dziewiec", "dziewiecdziesiat", "dziewiecdziesiat jeden", "dziewiecdziesiat dwa", "dziewiecdziesiat trzy", "dziewiecdziesiat cztery", "dziewiecdziesiat piec", "dziewiecdziesiat szesc", "dziewiecdziesiat siedem", "dziewiecdziesiat osiem", "dziewiecdziesiat dziewiec", "sto"}; Table[ StringLength[t[[n]]], {n, 1, Length[t]}] (* Artur Jasinski *)

Values re-calculated by R. Chandler - R. J. Mathar, Oct 17 2010

A178823 a(1) = 1, a(n+1) = least k >= a(n) such that the sum of the number of letters in the English name of all values in the sequence through a(n), excluding spaces and hyphens (A005589), is prime.

Original entry on oeis.org

1, 4, 5, 11, 12, 13, 24, 73, 1103, 1115, 1117, 1117, 1117, 1117, 1117, 1140, 1144, 1201, 1217, 1217, 1323, 1326, 1340, 1344, 1374, 1413, 1413, 1413, 1413, 1424, 1441, 1441, 1480, 1484

Offset: 1

Jonathan Vos Post, Dec 26 2010

			a(1) = 1 by definition.
a(2) = 4 because "one" plus "four" has 3 + 4 = 7 letters, with 7 prime.
a(3) = 5 because "one" plus "four" plus "five" gives 3 + 4 + 4 = 11, a prime.
a(4) = 11 because "one" plus "four" plus "five" plus "eleven" gives 3 + 4 + 4 + 6 = 17 is prime.
a(5) = 12 because "one" plus "four" plus "five" plus "eleven" plus "twelve" gives 3 + 4 + 4 + 6 + 6 = 23 is prime.
a(6) = 13 because "one" plus "four" plus "five" plus "eleven" plus "twelve" plus "thirteen" gives 3 + 4 + 4 + 6 + 6 + 8 = 31 is prime.
a(7) = 24 because "one" plus "four" plus "five" plus "eleven" plus "twelve" plus "thirteen" plus "twentyfour" gives 3 + 4 + 4 + 6 + 6 + 8 + 10 = 41 is prime.
a(8) = 73 because "one" plus "four" plus "five" plus "eleven" plus "twelve" plus "thirteen" plus "twentyfour" plus "seventythree" gives 3 + 4 + 4 + 6 + 6 + 8 + 10 + 12 = 53 is prime.
a(9) = 1103 because "one" plus "four" plus "five" plus "eleven" plus "twelve" plus "thirteen" plus "twentyfour" plus "seventythree" plus "one thousand one hundred three" gives 3 + 4 + 4 + 6 + 6 + 8 + 10 + 12 + 26 = 79 is prime.
a(10) = 1115 "one" plus "four" plus "five" plus "eleven" plus "twelve" plus "thirteen" plus "twentyfour" plus "seventythree" plus "one thousand one hundred three" plus "one thousand one hundred fifteen" gives 3 + 4 + 4 + 6 + 6 + 8 + 10 + 12 + 26 + 28 = 107 is prime.

Cf. A006944 (ordinals), A052360, A052362-A052363, A005589, A134629, A133418, A016037

a(11)-a(34) from Nathaniel Johnston, Jan 04 2011

A268490 Spelling out the characters (digits and commas) of the sequence and replacing letters A..Z with numbers 1..26 gives back the sequence.

Original entry on oeis.org

20, 23, 15, 26, 5, 18, 15, 3, 15, 13, 13, 1, 20, 23, 15, 20, 8, 18, 5, 5, 3, 15, 13, 13, 1, 15, 14, 5, 6, 9, 22, 5, 3, 15, 13, 13, 1, 20, 23, 15, 19, 9, 24, 3, 15, 13, 13, 1, 6, 9, 22, 5, 3, 15, 13, 13, 1, 15, 14, 5, 5, 9, 7, 8, 20, 3, 15, 13, 13, 1, 15, 14, 5, 6, 9, 22, 5, 3, 15, 13, 13, 1, 20, 8, 18, 5, 5, 3, 15, 13, 13, 1, 15, 14, 5, 6, 9, 22, 5, 3, 15, 13, 13, 1, 15, 14, 5, 20, 8

Offset: 1

M. F. Hasler, Feb 06 2016

A sequence with this property cannot start otherwise since 2 is the only digit equal to the first digit of the "code" (1-26) of the first letter of its English name.

			Spelling out the sequence data character-wise yields "two zero comma two three comma one five ..."
Coding the letters A..Z by 1..26 yields again the sequence 20, 23, 15, 26, 5, 18, 15, 3, 15, 13, 13, ...

Cf. A104059, A073029, A131744.

concat(apply(f=t->Vec(Vecsmall(concat(concat(apply(English,digits(t))),"comma")))%32,f(20))) \\ See A052360 for English()

cp's OEIS Frontend

A266851 The last letter of the English name of a(n) equals the a(n)-th letter of the concatenation of all the terms spelled out in English.

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A082655 Number of distinct letters needed to spell English names of numbers 1 through n.

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A118622 Numbers whose English names are 5 letters long.

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A132204 Sum of the numerical equivalents for the 23 Latin letters, according to Tartaglia, of the letters in the English name of n, excluding spaces and hyphens.

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A175725 Number of characters in the Polish name of n, including spaces and hyphens.

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A178823 a(1) = 1, a(n+1) = least k >= a(n) such that the sum of the number of letters in the English name of all values in the sequence through a(n), excluding spaces and hyphens (A005589), is prime.

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A268490 Spelling out the characters (digits and commas) of the sequence and replacing letters A..Z with numbers 1..26 gives back the sequence.

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PARI