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Search: id:A078563
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| A078563 |
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a(n) = the least positive integer N such that g(N) = n g(N-1), where g(k) = prime(k+1)-prime(k). |
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1
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| 3, 2, 11, 1022, 34, 46, 4714, 295, 99, 14372, 297, 263, 40026, 429, 985, 161441, 1457, 3087, 413695, 2344, 1879, 278832, 14939, 8423, 887313, 2810, 4260, 3589373, 7810, 13820
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OFFSET
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1,1
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COMMENT
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Conjecture: The equation g(N) = n g(N-1), for a fixed positive integer n, is always solvable for N.
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EXAMPLE
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N = 2 is the least positive integer such that g(N) = 2 = 2(1) = 2 g(N-1), so a(2) = 2.
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MATHEMATICA
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pg[n_] := Module[{r = 0, i = 2, a, b, c, p = False}, While[ ! p, a = Prime[i - 1]; b = Prime[i]; c = Prime[i + 1]; If[c - b == n (b - a), r = i; p = True]; i = i + 1]; r]; Table[pg[i], {i, 1, 30}]
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CROSSREFS
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Sequence in context: A087956 A116391 A087629 this_sequence A016560 A122407 A098646
Adjacent sequences: A078560 A078561 A078562 this_sequence A078564 A078565 A078566
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KEYWORD
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nonn
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AUTHOR
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Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Jan 07 2003
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