A045736 Smallest positive integer requiring n syllables to pronounce in American English.

1, 7, 11, 27, 77, 111, 127, 177, 777, 1127, 1177, 1777, 7777, 11777, 27777, 77777, 111777, 127777, 177777, 777777, 1127777, 1177777, 1777777, 7777777, 11777777, 27777777, 77777777, 111777777, 127777777, 177777777, 777777777, 1127777777

Offset

1,2

Comments

Assumes the American usage of billion, trillion, etc. ("short scale"), which makes a difference from a(59) on.

See A002810 for the British English version, which in particular includes the additional "and", e.g., in "one hundred and seven". Therefore the sequences differ from a(6)=111 on, with A002810(6)= 107. - M. F. Hasler, Nov 03 2013

Links

Table of n, a(n) for n=1..32.

Robert G. Wilson v, English names for the numbers from 0 to 11159 without spaces or hyphens.

Index to OEIS: sequences related to English words for n

Formula

a(n) = min{ k | A075774(k)=n }. - M. F. Hasler, Nov 03 2013

a(n+11) = a(n)*1000+777, as long as a(n+11) is less than one quadrillion (whatever scale is used). - M. F. Hasler, Nov 03 2013

Prog

(PARI) A045736(n)={n>11 || for(k=1, 1e5, A075774(k)==n && return(k)); A045736(n-11*n=(n-1)\11)*1000^n+1000^n\9*7 } \\ This code is valid up to n=58 (short scale) or n=82 (long scale). - M. F. Hasler, Nov 03 2013

Crossrefs

Cf. A002810.

Sequence in context: A039287 A045222 A002810 * A158807 A338929 A067006

Adjacent sequences: A045733 A045734 A045735 * A045737 A045738 A045739

Keyword

nonn,word

Author

Brian Galebach

Status

approved