A121065 - OEIS

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

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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)