A121065 a(n) is the smallest number in English which contains n letter 'E's.

2, 0, 3, 11, 17, 111, 117, 317, 1317, 3317, 11317, 17317, 111317, 117317, 317317, 1317317, 3317317, 11317317, 17317317, 111317317, 117317317, 317317317, 1317317317, 3317317317, 11317317317, 17317317317, 111317317317, 117317317317, 317317317317, 1317317317317

Offset: 0

Author

Ray G. Opao, Aug 10 2006

Keywords

• nonn
• word

Comments

4, 5, 6, 8, 9 never appear in any of these numbers because in each case there is a smaller digit with the same number of e's. 2 (the smallest number with no e's) never appears in any term after a(0). - Sean A. Irvine, Nov 10 2009

A085513(a(n)) = n and A085513(m) != n for m < a(n). - Reinhard Zumkeller, Jan 24 2015

Examples

			a(2) = THREE, which has two Es.
		

Links

• Index entries for sequences related to number of letters in n

Crossrefs

Cf. A085513, A008520, A006933. Variant of A036448.

Programs

Haskell

import Data.List (elemIndex); import Data.Maybe (fromJust)
a121065 = fromJust . (`elemIndex` a085513_list)
-- Reinhard Zumkeller, Jan 24 2015

Formula

From Chai Wah Wu, Dec 20 2019: (Start)

a(n) = a(n-1) + 1000*a(n-7) - 1000*a(n-8) for n > 9 (conjectured).

G.f.: (-1000*x^9 + 3000*x^8 - 1800*x^7 + 6*x^6 + 94*x^5 + 6*x^4 + 8*x^3 + 3*x^2 - 2*x + 2)/((x - 1)*(1000*x^7 - 1)) (conjectured). (End)

Extensions

More terms Sean A. Irvine, Nov 10 2009

a(19) - a(21) added by Reinhard Zumkeller, Jan 24 2015

a(22) - a(29) from Chai Wah Wu, Dec 20 2019