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A076368
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a(1) = 1; for n > 1, a(n) = prime(n)-prime(n-1)+1.
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6
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1, 2, 3, 3, 5, 3, 5, 3, 5, 7, 3, 7, 5, 3, 5, 7, 7, 3, 7, 5, 3, 7, 5, 7, 9, 5, 3, 5, 3, 5, 15, 5, 7, 3, 11, 3, 7, 7, 5, 7, 7, 3, 11, 3, 5, 3, 13, 13, 5, 3, 5, 7, 3, 11, 7, 7, 7, 3, 7, 5, 3, 11, 15, 5, 3, 5, 15, 7, 11, 3, 5, 7, 9, 7, 7, 5, 7, 9, 5, 9, 11, 3, 11, 3, 7, 5, 7, 9, 5, 3, 5, 13, 9, 5, 9, 5, 7
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Counts[occurrences] of n in A060646 or n-th prime in A076367.
Sequences A060646, A076367, A076368 was used in proof a property of 30. See A048597, A060646 and corresponding References. It is provable[Bonse] that a(n)>=3 if n>3.
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MATHEMATICA
| c[x_, j_] := x+1-(j+Prime[j])c[x, 0]=x; a=1000; t=Table[0, {a}]; t1=Table[0, {a}]; Table[fl=1; (*Print["% ", u, " #"]; *)Do[s=c[u, n]; If[Equal[fl, 1]&&Equal[Sign[s], -1], Print[n]; t[[u]]=n; t1[[u]]=Prime[n]; fl=0], {n, 1, u}], {u, 1, a}]//t (*=A060646*)//t1 (*=A076367*) Table[Count[t, j], {j, 1, PrimePi[a]}]
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CROSSREFS
| Cf. A048597, A060646, A076367. See also A076366.
Cf. A000040, A001223.
Sequence in context: A063256 A131320 A119912 * A071049 A171637 A140187
Adjacent sequences: A076365 A076366 A076367 * A076369 A076370 A076371
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Oct 14 2002
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EXTENSIONS
| Simpler description from Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 29 2003
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