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A370254 a(0) = 1, a(n) = result of eliminating the digit 7 from the sum of all previous terms for n>=1.

%I A370254 #32 Feb 19 2024 03:32:41
%S A370254 1,1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384,3268,36036,
%T A370254 202,224,2498,4996,9992,89984,19968,199936,39982,439854,8908,888616,
%U A370254 1232,18464,196928,1993856,39812,402524,4430048,8860096,120192,1840384,1968068
%N A370254 a(0) = 1, a(n) = result of eliminating the digit 7 from the sum of all previous terms for n>=1.
%H A370254 Alois P. Heinz, <a href="/A370254/b370254.txt">Table of n, a(n) for n = 0..16384</a>
%F A370254 a(n) = A004182(Sum_{i=0..n-1} a(i)) for n >= 1, a(0) = 1.
%F A370254 a(n) = A011782(n) for n <= 15.
%e A370254 a(16) = 3268 since the sum of a(0)..a(15) = 32768. Eliminating the "7" we get 3268.
%p A370254 a:= proc(n) option remember; `if`(n=0, 1, (l-> add(l[i]*10^(i-1),
%p A370254       i=1..nops(l)))(subs(7=NULL, convert(s(n-1), base, 10))))
%p A370254     end:
%p A370254 s:= proc(n) option remember; `if`(n<0, 0, s(n-1)+a(n)) end:
%p A370254 seq(a(n), n=0..40);  # _Alois P. Heinz_, Feb 15 2024
%t A370254 Module[{nmax=50, s=1, a}, NestList[(s+=(a=FromDigits[DeleteCases[IntegerDigits[s], 7]]); a) &, s, nmax]] (* _Paolo Xausa_, Feb 19 2024 *)
%o A370254 (PARI) lista(nn) = my(va = vector(nn)); va[1] = 1; for (n=2, nn, va[n] = sum(k=1, n-1, va[k]); my(d=digits(va[n])); if (vecsearch(Set(d), 7), my(list = List()); for (i=1, #d, if (d[i] !=7, listput(list, d[i]));); va[n] = fromdigits(Vec(list)););); va; \\ _Michel Marcus_, Feb 13 2024
%Y A370254 Cf. A004182, A011782, A069638, A108566.
%K A370254 nonn,look,base
%O A370254 0,3
%A A370254 _Sergio Pimentel_, Feb 13 2024