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

0,1

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

Links

Table of n, a(n) for n=0..29.

Index entries for sequences related to number of letters in n

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)

Example

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

Prog

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

Crossrefs

Cf. A085513, A008520, A006933.

Sequence in context: A365985 A327244 A325816 * A077928 A105418 A368584

Adjacent sequences: A121062 A121063 A121064 * A121066 A121067 A121068

Keyword

nonn,word

Author

Ray G. Opao, Aug 10 2006

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

Status

approved