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A086537 Beginning with 1, the smallest number such that every partial sum has a distinct prime signature. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Conjecture: this is a rearrangement of natural numbers (i.e. every natural number is a member).
LINKS
EXAMPLE
The partial sums are 1, 3, 6, 12, 16, 24, 36, 49, 54, ... (A086538), each with a distinct prime signature.
PROG
(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
CROSSREFS
Cf. A086538.
Sequence in context: A289055 A109890 A370046 * A212486 A127562 A096113
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Aug 19 2003
EXTENSIONS
More terms from David Wasserman, Mar 15 2005
Duplicate example deleted by Harvey P. Dale, Jun 17 2023
STATUS
approved

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Last modified March 19 06:29 EDT 2024. Contains 370953 sequences. (Running on oeis4.)