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A086537
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Beginning with 1, the smallest number such that every partial sum has a distinct prime signature.
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1
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Conjecture: this is a rearrangement of natural numbers (i.e. every natural number is a member).
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EXAMPLE
| The partial sums are 1, 3, 6, 12, 16, 24, 36, 49, 54, ... (A086538), each with a distinct prime signature.
The partial sums are 1, 3, 6, 12, 16, 24, 36, 49, ... (A086538), each with a distinct prime signature.
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PROG
| (PARI) print(1); ps(n) = local(f); f = factor(n); vecsort(f[, 2]); P = vector(70); psUsed(v, n) = for (i = 1, n - 1, if (v == P[i], return(1))); 0; 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; print(i); while(used[x], x++)); (Wasserman)
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CROSSREFS
| Cf. A086538.
Sequence in context: A132169 A112975 A109890 * A127562 A096113 A110797
Adjacent sequences: A086534 A086535 A086536 * A086538 A086539 A086540
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KEYWORD
| nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Aug 19 2003
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EXTENSIONS
| More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Mar 15 2005
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