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A300730
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Positive integers j of the form Sum_{i=1..k} b(i)c(i), i.e., not in A297345 such that there is only one set {c(1),...,c(k)} where the c(i) are drawn with repetition from {b(0),...,b(k)} and b(k+1) is the smallest element of A297345 that is larger than j, where b() is A297345.
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0
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3, 5, 6, 8, 10, 12, 13, 17, 19, 20, 22, 27, 32, 34, 36, 37, 41, 43, 44, 46, 61, 67, 68, 82, 84, 91, 95, 107, 119, 126, 129, 131, 153, 167, 204, 211, 214, 252, 261, 416, 452, 489, 499, 537, 6006, 6265, 6266, 6312, 190852, 207403, 208524, 208806, 211967, 213074, 213594, 213677, 214781, 215042, 215075, 215077
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OFFSET
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1,1
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LINKS
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Table of n, a(n) for n=1..60.
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EXAMPLE
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The first positive integer not in b() is 3. To check if 3 is a(1) we note that the smallest element of b() larger than 3 is b(3)=7, hence k=2. There is only one set of coefficients {c(1),c(2)} that allows 3 to be obtained from Sum_{i=1..k} b(i)c(i). These are c(1)=2 and c(2)=1. So 3 is in fact a(1).
The next integer not in b() is 4. To see if it is a(2) we note that k is still 2 in this case. Now there are two possible sets of coefficients that allow the representation of 4: {0,2} and {2,1}, so 4 is not a term.
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PROG
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(Python)
# generates all elements of the sequence, smaller than 6268
import numpy as np
import itertools
def g(i, s, perms):
c = 0
for iks in perms:
t=np.asarray(iks)
if np.dot(t, s) == i:
c += 1
if c == 2:
break
if c == 1:
print i
S=[1, 2, 7, 24, 85, 285, 1143]
S1=[0, 1, 2, 7, 24, 85, 285, 1143]
perms = [p for p in itertools.product(S1, repeat=len(S))]
s=np.asarray(S, dtype=np.int)
for i in range(1, 6268):
if i not in S:
g(i, s, perms)
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CROSSREFS
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Cf. A297345.
Sequence in context: A329841 A047329 A187685 * A191777 A284590 A287724
Adjacent sequences: A300727 A300728 A300729 * A300731 A300732 A300733
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KEYWORD
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nonn
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AUTHOR
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Luis F.B.A. Alexandre, Mar 11 2018
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STATUS
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approved
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