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, 1177777777, 1777777777

Offset: 1

Author

Brian Galebach

Keywords

• nonn
• word

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

• 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

Crossrefs

Cf. A002810.

Programs

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

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