A303475 a(n) is the least m > n, such that every letter, with repetition, that occurs in the English name of n also occurs in the English name of m.

14, 21, 13, 14, 25, 16, 17, 18, 19, 13, 111, 112, 37, 74, 57, 67, 77, 78, 79, 21, 120, 122, 122, 124, 125, 126, 127, 128, 125, 31, 125, 128, 132, 134, 135, 136, 137, 138, 135, 41, 124, 124, 124, 144, 145, 64, 74, 148, 94, 51, 145, 152, 152, 154, 155, 156, 157, 158, 155, 61

Offset

1,1

Links

Altug Alkan, Table of n, a(n) for n = 1..10000

Example

a(2)=21 because 2 is two, and 21 is twenty-one, where all letters of two appear in twenty-one, and this does not happen before 21.

Mathematica

in[n_]:=IntegerName[n, "Words"];
ch[n_]:=Characters[StringReplace[IntegerName[n, "Words"], {"-"->"", " "->""}]];
f[n_]:=Module[{m=n+1}, While[Complement[ch[n], ch[m]]!={}||
Union[Select[Table[Count[ch[m], ch[n][[i]]]-Count[ch[n], ch[n][[i]]], {i, 1, Length[ch[n]]}], #<0&]]!={}, m++]; m];
Array[f, 60] (* Ivan N. Ianakiev, Apr 26 2018 *)

Prog

(PARI)
v1 = ["one", "two", "three", "four", "five", "six", "seven", "eight", "nine"];
v2 = ["eleven", "twelve", "thirteen", "fourteen", "fifteen", "sixteen", "seventeen", "eighteen", "nineteen"];
v3 = ["ten", "twenty", "thirty", "forty", "fifty", "sixty", "seventy", "eighty", "ninety"];
conv(n) = {if (n >= 10^12, error("too big for this program"));
if (n >= 10^9, return (concat(concat(conv(n\10^6), "billion"), conv(n % 10^9))));
if (n >= 10^6, return (concat(concat(conv(n\10^6), "million"), conv(n % 10^6))));
if (n >= 10^3, return (concat(concat(conv(n\10^3), "thousand"), conv(n % 10^3))));
if (n >= 10^2, return (concat(concat(conv(n\100), "hundred"), conv(n % 100))));
if (n >= 20, return (concat(v3[n\10], conv(n%10))); );
if (n >= 10, if (n==10, return(v3[n\10]), return(v2[n % 10])); );
if (n, return(v1[n]), return (""));
}
mycmp(sa, sb) = {my(vsa = Vec(sa), vsb = Vec(sb), vsas = vecsort(vsa, , 8)); for (i=1, #vsas, if (#select(x->x==vsas[i], vsb) < #select(x->x==vsas[i], vsa), return (0)); ); return (1); }
a(n) = {my(m = n+1, sn = conv(n), sm = conv(m)); while(! mycmp(sn, sm), m++; sm = conv(m)); m; }

Crossrefs

Cf. A303380.

Sequence in context: A129244 A070719 A030643 * A028395 A167170 A213536

Adjacent sequences: A303472 A303473 A303474 * A303476 A303477 A303478

Keyword

nonn,word,look

Author

Michel Marcus, Apr 24 2018

Status

approved