The distribution of zeroes zeros is the same as in A276204.

proposed

approved

editing

proposed

Cf. A276204 defined similarly but with arithmetic progression of length 3.

Cf. A276205 defined similarly but with arithmetic progression of length 4.

Cf. A276206 defined similarly but with arithmetic progression of length 5.

Cf. A276204 (length 3), A276205 (length 4), A276206 (length 5).

proposed

editing

editing

proposed

a(0) = a(1) = 0 and for . For n>1 a(n) is the smallest nonnegative integer such that there is no arithmetic progression m_1,m_2,...,m_i,n (2<=i<n) such that a(m_1)+a(m_2)+...+a(m_i) = a(n).

0, 0, 1, 0, 0, 2, 4, 1, 1, 0, 0, 5, 0, 0, 3, 7, 2, 3, 2, 4, 1, 1, 12, 1, 5, 1, 1, 0, 0, 13, 0, 0, 10, 9, 6, 7, 0, 0, 18, 0, 0, 15, 4, 14, 7, 6, 8, 2, 6, 3, 16, 3, 3, 2, 3, 7, 1, 10, 25, 8, 5, 1, 1, 1, 4, 14, 27, 4, 1, 1, 10, 2, 2, 6, 1, 26, 8, 1, 19, 1, 1, 0, 0, 13, 0, 0, 7, 24, 2, 19, 0, 0, 34, 0, 0, 29, 32, 32, 5, 15, 21, 14, 15, 6, 6, 24, 13, 39, 0, 0, 24, 0, 0, 14, 12, 12, 34, 0, 0, 23, 0, 0, 7, 5, 20, 3, 8, 3, 22, 12, 9, 12, 4, 5, 11, 4, 27, 11, 9, 11, 11, 18, 24, 5, 6, 10, 48, 13, 28, 11, 6, 36, 1, 16, 41, 6, 17, 7, 3, 6, 2, 2, 6, 5, 1, 4, 4, 5, 4, 1, 1, 9, 58, 23, 9, 61, 1, 45, 2, 50, 2, 3, 1, 62, 2, 1, 31, 12, 1, 1, 67, 8, 2, 33, 1, 26, 20, 2, 86, 47, 1, 47, 8, 35, 20, 1, 1

One can easily notice the The distribution of zeroes is the same as in A276204.

for For n = 5 we have that:

there is no such arithmetic progression m_1,m_2,...,m_i,5 that a(m_1)+a(m_2)+...+a(m_i)=2, so a(5) = 2.

Cf. A276204 defined similarly but with arithmetic progression of length 3.

Cf. A276205 defined similarly but with arithmetic progression of length 4.

Cf. A276206 defined similarly but with arithmetic progression of length 5.

nonn,unkn,uned,changed

proposed

editing

editing

proposed

Michal Urbanski, <a href="/A276207/b276207.txt">Table of n, a(n) for n = 0..49999</a>

A276204 defined similarly but with arithmetic progression of length 3

allocated a(0)=a(1)=0 and for Michal Urbanskin>1 a(n) is the smallest nonnegative integer such that there is no arithmetic progression m_1,m_2,...,m_i,n (2<=i<n) such that a(m_1)+a(m_2)+...+a(m_i)=a(n)

0, 0, 1, 0, 0, 2, 4, 1, 1, 0, 0, 5, 0, 0, 3, 7, 2, 3, 2, 4, 1, 1, 12, 1, 5, 1, 1, 0, 0, 13, 0, 0, 10, 9, 6, 7, 0, 0, 18, 0, 0, 15, 4, 14, 7, 6, 8, 2, 6, 3, 16, 3, 3, 2, 3, 7, 1, 10, 25, 8, 5, 1, 1, 1, 4, 14, 27, 4, 1, 1, 10, 2, 2, 6, 1, 26, 8, 1, 19, 1, 1, 0, 0, 13, 0, 0, 7, 24, 2, 19, 0, 0, 34, 0, 0, 29, 32, 32, 5, 15, 21, 14, 15, 6, 6, 24, 13, 39, 0, 0, 24, 0, 0, 14, 12, 12, 34, 0, 0, 23, 0, 0, 7, 5, 20, 3, 8, 3, 22, 12, 9, 12, 4, 5, 11, 4, 27, 11, 9, 11, 11, 18, 24, 5, 6, 10, 48, 13, 28, 11, 6, 36, 1, 16, 41, 6, 17, 7, 3, 6, 2, 2, 6, 5, 1, 4, 4, 5, 4, 1, 1, 9, 58, 23, 9, 61, 1, 45, 2, 50, 2, 3, 1, 62, 2, 1, 31, 12, 1, 1, 67, 8, 2, 33, 1, 26, 20, 2, 86, 47, 1, 47, 8, 35, 20, 1, 1

0,6

One can easily notice the distribution of zeroes is the same as in A276204

for n=5

a(5)>0, because a(3)+a(4)=0 and 3,4,5 is an arithmetic progression

a(5)>1, because a(2)+a(3)+a(4)=1 and 2,3,4,5 is an arithmetic progression

there is no such arithmetic progression m_1,m_2,...,m_i,5 that a(m_1)+a(m_2)+...+a(m_i)=2, so a(5)=2

A276204 defined similarly but with arithmetic progression of length 3

A276205 defined similarly but with arithmetic progression of length 4

A276206 defined similarly but with arithmetic progression of length 5

allocated

nonn,unkn,uned

Michal Urbanski, Aug 24 2016

approved

editing

allocated for Michal Urbanski

allocated

approved