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

1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 3268, 36036, 202, 224, 2498, 4996, 9992, 89984, 19968, 199936, 39982, 439854, 8908, 888616, 1232, 18464, 196928, 1993856, 39812, 402524, 4430048, 8860096, 120192, 1840384, 1968068

Offset: 0

Author

Sergio Pimentel, Feb 13 2024

Keywords

• nonn
• look
• base

Examples

			a(16) = 3268 since the sum of a(0)..a(15) = 32768. Eliminating the "7" we get 3268.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..16384

Crossrefs

Cf. A004182, A011782, A069638, A108566.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, (l-> add(l[i]*10^(i-1),
      i=1..nops(l)))(subs(7=NULL, convert(s(n-1), base, 10))))
    end:
s:= proc(n) option remember; `if`(n<0, 0, s(n-1)+a(n)) end:
seq(a(n), n=0..40);  # Alois P. Heinz, Feb 15 2024

Mathematica

Module[{nmax=50, s=1, a}, NestList[(s+=(a=FromDigits[DeleteCases[IntegerDigits[s], 7]]); a) &, s, nmax]] (* Paolo Xausa, Feb 19 2024 *)

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

Formula

a(n) = A004182(Sum_{i=0..n-1} a(i)) for n >= 1, a(0) = 1.

a(n) = A011782(n) for n <= 15.