A003158 -id:A003158 - cp's OEIS frontend

A138001 Numbers not representable as sum of elements of A138000.

1, 4, 6, 8, 15, 17, 19, 22, 24, 25, 26, 27, 28, 30, 33, 35, 37, 44, 46, 48, 51, 54, 57, 59, 61, 68, 70, 72, 75, 77, 78, 79, 80, 81, 83, 86, 88, 90, 97, 99, 101, 104, 106, 108, 111, 113, 115, 122, 124, 126, 129, 131, 132, 133, 134, 135, 137, 140, 142, 144, 151, 153, 155

Offset: 1

M. F. Hasler, Apr 09 2008

nonn

Let R(0)={0} and for n>0, R(n) = R(n-1) union A138000(n)+R(n-1) be the numbers which can be written as sum of some subset of {A138000(1),...,A138000(n)}. A138001 is then the complement of R=union( R(n), n>0) in N.

			A138000=(2,3,7,11,...) and increasing, thus 1,4,6,8,... cannot be written as sum of elements of A138000. To get the numbers which have to be omitted, construct the sets R(1),R(2),... as defined in the comment.

Cf. A138000, A064934, A003158.

s=p=q=1; for( n=1,9, while( bitand( s, s>>p=nextprime(p+1)),); s+=s<p, bittest( s,q ) || print1( q",")))

A138001 = N \ { A138000(k[1])+...+ A138000(k[m]) ; m>=0, 0

A296371 Number of integer partitions of n using Jacobsthal numbers.

Original entry on oeis.org

1, 1, 1, 2, 2, 3, 4, 4, 5, 6, 7, 9, 10, 11, 13, 15, 17, 19, 21, 23, 26, 30, 33, 36, 40, 44, 49, 54, 58, 63, 69, 75, 82, 89, 95, 103, 112, 120, 129, 138, 147, 158, 170, 182, 194, 207, 221, 236, 252, 267, 283, 301, 319, 339, 360, 380, 402, 426, 450, 475, 501, 527

Offset: 0

Gus Wiseman, Dec 11 2017

nonn

			The a(10) = 7 partitions are (1111111111), (31111111), (331111), (3331), (511111), (5311), (55).

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Cf. A000041, A001045, A003158, A018819, A050377, A197911.

nn=6;
jac[n_]:=(2^n-(-1)^n)/3;
Table[SeriesCoefficient[Product[1/(1-x^jac[i]),{i,2,nn}],{x,0,n}],{n,jac[nn]}]

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A138001 Numbers not representable as sum of elements of A138000.

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