A244671 The lexicographically earliest increasing sequence such that a(n) divides the sum of the first a(n) terms.

1, 3, 5, 6, 10, 11, 12, 13, 14, 15, 20, 22, 24, 26, 28, 29, 30, 31, 32, 48, 49, 55, 56, 60, 61, 67, 68, 72, 89, 93, 97, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 141, 161, 162, 163, 164, 165, 166, 175, 188, 189, 190, 191, 222, 269

Offset

1,2

Comments

See A244672(n) - partial sums of a(n).

Links

Table of n, a(n) for n=1..61.

Formula

A244672(a(n)) / a(n) = integer.

Example

a(1) = 1 because 1 divides the first term (1/1=1); a(2) cannot be 2 because 2 does not divide the sum of the first 2 terms (3/2 is not integer), a(2) must be 3; if a(2) = 3 then a(3) must be 5 (5 is the smallest number > a(2) such that the sum of the first 3 terms (i.e. 9) is divisible by a(2) = 3; if a(4) = 6 (holds 6 > a(3)), a(5) must be 10 (10 is the smallest number > a(4) such that the sum of first 5 terms (i.e. 25) is divisible by a(3) = 5; etc…

Maple

N:= 1000: # to get the first N terms
A:= {1, 3}: s:= 4:
for n from 3 to N do
  if member(n, A, 'p') then
     r:= A[n-1]+1 + (-s-A[n-1]-1 mod A[p])
  else
     r:= A[n-1]+1
  fi;
  A:= A union {r};
  s:= s + r;
od:
A; # Robert Israel, Jul 06 2014

Crossrefs

Cf. A243700, A244672.

Sequence in context: A248644 A242197 A283051 * A232531 A182637 A331915

Adjacent sequences: A244668 A244669 A244670 * A244672 A244673 A244674

Keyword

nonn

Author

Jaroslav Krizek, Jul 04 2014

Status

approved