A308405 Numbers k such that k, when written in English, has 1 letter more than k+1.

3, 5, 8, 9, 14, 17, 23, 25, 28, 33, 35, 38, 43, 45, 48, 53, 55, 58, 63, 65, 68, 73, 75, 78, 83, 85, 88, 93, 95, 98, 103, 105, 108, 109, 114, 117, 123, 125, 128, 133, 135, 138, 143, 145, 148, 153, 155, 158, 163, 165, 168, 173, 175, 178, 183, 185, 188, 193, 195

Offset

1,1

Links

Table of n, a(n) for n=1..59.

Example

a(1) = 3 = THREE has 1 letter more than a(1) + 1 = FOUR;
a(2) = 5 = FIVE has 1 letter more than a(2) + 1 = SIX;
a(3) = 8 = EIGHT has 1 letter more than a(3) + 1 = NINE;
a(4) = 9 = NINE has 1 letter more than a(4) + 1 = TEN;
a(5) = 14 = FOURTEEN has 1 letter more than a(5) + 1 = FIFTEEN; etc.

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 (""));
} \\ after Michel Marcus in A303475
is(n) = #conv(n)-1==#conv(n+1) \\ Felix Fröhlich, May 25 2019

Crossrefs

Sequence in context: A137319 A138808 A185456 * A331314 A018804 A032682

Adjacent sequences: A308402 A308403 A308404 * A308406 A308407 A308408

Keyword

nonn,word

Author

Eric Angelini, May 25 2019

Extensions

17 and terms beyond 98 from Felix Fröhlich, May 25 2019

Status

approved