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A086537
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Beginning with 1, the smallest number not yet seen such that every partial sum has a distinct prime signature.
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2
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1, 2, 3, 6, 4, 8, 12, 13, 11, 10, 26, 16, 32, 24, 42, 30, 48, 55, 17, 36, 52, 64, 118, 18, 27, 45, 9, 39, 72, 56, 104, 80, 40, 140, 84, 96, 160, 128, 192, 240, 144, 216, 120, 60, 180, 245, 75, 256, 114, 14, 304, 112, 320, 288, 292, 220, 280, 360, 384, 156, 261, 159, 210
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OFFSET
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1,2
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COMMENTS
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Conjecture: this is a rearrangement of natural numbers (i.e., every natural number is a term).
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LINKS
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EXAMPLE
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The partial sums are 1, 3, 6, 12, 16, 24, 36, 49, 54, ... (A086538), each with a distinct prime signature.
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MAPLE
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ps:= proc(n) local F;
F:= ifactors(n)[2];
sort(F[.., 2])
end proc:
N:= 1000: # for terms before the first term > N
Cands:= [$1..N]:
R:= NULL: s:= 0: Sigs:= {}: found:= true:
for count from 1 while found do
found:= false;
for i from 1 to N+1-count do
sp:= s+Cands[i];
x:= ps(sp);
if member(x, Sigs) then next fi;
R:= R, Cands[i];
Sigs:= Sigs union {x};
Cands:= subsop(i=NULL, Cands);
found:= true;
s:= sp;
break
od
od:
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PROG
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(PARI)
ps(n) = local(f); f = factor(n); vecsort(f[, 2]);
psUsed(v, n) = for (i = 1, n - 1, if (v == P[i], return(1))); 0;
print1(1, ", "); P = vector(70); used = vector(10000); x = 2; s = 1; for (n = 1, 70, i = x; v = ps(s + i); while (psUsed(v, n), i++; while (used[i], i++); v = ps(s + i)); used[i] = 1; P[n] = v; s += i; print1(i, ", "); while(used[x], x++)); \\ David Wasserman, Mar 15 2005
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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