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A244671
The lexicographically earliest increasing sequence such that a(n) divides the sum of the first a(n) terms.
2
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).
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
Sequence in context: A242197 A283051 A376377 * A232531 A182637 A331915
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Jul 04 2014
STATUS
approved