This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A297345 a(0)=0; for n>0, a(n) is the least positive integer that cannot be represented as Sum_{k=1..n-1} a(i_k)*a(k), with 0 <= i_k < n. 1
 0, 1, 2, 7, 24, 85, 285, 1143, 6268, 216784, 1059813, 6100794, 226303113 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS EXAMPLE a(1)= 1 since it is not possible to write 1 using only a(0). a(2)=2, since it is not possible to obtain 2 using only a(0) and a(1). The following numbers up to 6 can be represented using these first 3 elements of the sequence: 3 = 1*1 + 1*2, 4 = 0*1 + 2*2, 5 = 1*1 + 2*2, 6 = 2*1 + 2*2. Again we reach a number that cannot be represented as defined above, so that number is appended to the sequence. It happens here when we try to represent 7 using only a(0)=0, a(1)=1, and a(2)=2. So 7 becomes a(3). A larger example: 216752 = 1*1 + 1*2 + 85*7 + 285*24 + 85*85 + 85*285 + 24*1143 + 24*6268 MATHEMATICA Nest[Function[a, Append[a, 1 + LengthWhile[Differences@ #, # == 1 &] &@ Union[Total /@ Map[a # &, Tuples[a, Length@ a]]]]], {0}, 8] (* Michael De Vlieger, Jan 09 2018 *) PROG (Python) # Generate all the elements in the sequence, S, necessary to represent all # numbers until the integer 'last'. It also shows how each integer is # represented by showing the sequence elements and the respective # multiplicative factors. import numpy as np import itertools last=100 def generate(i, S):     n=len(S)     s=np.asarray(S, dtype=np.int)     perms = [p for p in itertools.product(S, repeat=n)]     for iks in perms:         t=np.asarray(iks)         if np.dot(t, s) == i:             print '%d=' %i,             print t, 'x', s             return 0     return -1 S=[0] for i in range(1, last+1):         if generate(i, S) == -1:             S.append(i)             generate(i, S) CROSSREFS Sequence in context: A088854 A000777 A144170 * A052986 A053368 A141753 Adjacent sequences:  A297342 A297343 A297344 * A297346 A297347 A297348 KEYWORD nonn,more,hard AUTHOR Luis F.B.A. Alexandre, Dec 28 2017 EXTENSIONS a(9) from Robert G. Wilson v, Jan 09 2018 a(10)-a(11) from Jon E. Schoenfield, Jan 16 2018 a(12) from Giovanni Resta, Jan 22 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 19 02:58 EDT 2019. Contains 322237 sequences. (Running on oeis4.)