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

Author

Jaroslav Krizek, Jul 04 2014

Keywords

• nonn

Comments

Partial sums give A244672.

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

Examples

			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 an 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...
		

Crossrefs

Cf. A243700, A244672.

Programs

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