A050620 -id:A050620 - cp's OEIS frontend

A035014 a(n) contains n digits (either '3' or '4') and is divisible by 2^n.

4, 44, 344, 3344, 33344, 433344, 3433344, 33433344, 333433344, 3333433344, 43333433344, 343333433344, 3343333433344, 33343333433344, 433343333433344, 3433343333433344, 43433343333433344, 443433343333433344, 3443433343333433344, 43443433343333433344

Offset: 1

J. Lowell

If (n-1)st term is divisible by 2^n, then n-th term begins with a 4. If not, then n-th term begins with a 3.

Proof of conjecture that a(n) ends with a(n-1): If a(n) is divisible by 2^n, then a(n) is divisible by 2^(n-1), so a(n)-k*10^(n-1) is divisible by 2^(n-1) for integer k, but if k is first digit of a(n) then a(n)-k*10^(n-1) is an (n-1)-digit number made up of 3s and 4s and divisible by 2^(n-1) and so must be a(n-1). - Henry Bottomley, Feb 14 2000

Ray Chandler, Table of n, a(n) for n = 1..1000 (first 100 terms from Jon E. Schoenfield)

Cf. A050620, A050621, A050622, A023402.

A035014 := proc(n)
    option remember ;
      local pre;
      if n = 1 then
        4;
    else
        pre := procname(n-1) ;
        pre+10^(n-1)*(4-modp(pre/2^(n-1),2)) ;
    end if;
end proc: # R. J. Mathar, May 02 2014

a(n) = if (n==1, 4, a(n-1) + 10^(n-1)*(4-(a(n-1)/2^(n-1) % 2))); \\ Michel Marcus, Apr 07 2017

a(n) = a(n-1) + 10^(n-1)*(4-[a(n-1)/2^(n-1) mod 2]), i.e., a(n) ends with a(n-1). - Henry Bottomley, Feb 14 2000

Corrected and extended by Patrick De Geest, Jun 15 1999

More terms from Henry Bottomley, Feb 14 2000

A055880 Quotients arising from sequence A053317.

Original entry on oeis.org

1, 13, 69, 347, 1736, 3993, 41059, 215842, 498546, 2202398, 10866824, 54261537, 637482331, 3370498978, 7788765114, 34411960682, 169793870966, 847836388608, 4238615459929, 49803023550277, 263320090876701, 1323752940946163

Offset: 1

J. Lowell, Jul 15 2000

Ray Chandler, Table of n, a(n) for n = 1..1431 (terms < 10^1000)

Cf. A023398, A053317, A050620.

a(n) = A053317(n)/2^n - David Wasserman, Apr 28 2002

More terms from David Wasserman, Apr 28 2002

cp's OEIS Frontend

A035014 a(n) contains n digits (either '3' or '4') and is divisible by 2^n.

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