A121065 - OEIS

%I #13 Dec 20 2019 22:22:09

%S 2,0,3,11,17,111,117,317,1317,3317,11317,17317,111317,117317,317317,

%T 1317317,3317317,11317317,17317317,111317317,117317317,317317317,

%U 1317317317,3317317317,11317317317,17317317317,111317317317,117317317317,317317317317,1317317317317

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

%C 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

%C A085513(a(n)) = n and A085513(m) != n for m < a(n). - _Reinhard Zumkeller_, Jan 24 2015

%H <a href="/index/Lc#letters">Index entries for sequences related to number of letters in n</a>

%F From _Chai Wah Wu_, Dec 20 2019: (Start)

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

%F 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)

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

%o (Haskell)

%o import Data.List (elemIndex); import Data.Maybe (fromJust)

%o a121065 = fromJust . (`elemIndex` a085513_list)

%o -- _Reinhard Zumkeller_, Jan 24 2015

%Y Cf. A085513, A008520, A006933.

%K nonn,word

%O 0,1

%A _Ray G. Opao_, Aug 10 2006

%E More terms _Sean A. Irvine_, Nov 10 2009

%E a(19) - a(21) added by _Reinhard Zumkeller_, Jan 24 2015

%E a(22) - a(29) from _Chai Wah Wu_, Dec 20 2019