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A066496
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a(n) = least solution k of f(k) = f(k-1) + ... + f(k-n), where f(m) = prime(m+1)-prime(m) and prime(m) denotes the m-th prime, if k exists; 0 otherwise.
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1
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3, 4, 114, 852, 1648, 1847, 2500, 22765, 54954, 59930, 47350, 971579, 2183012, 1945709, 14424271, 19139070, 19517159, 122815056, 318016298, 72732221, 575945350, 1020650071, 3009991871, 3411065961, 9193759213, 847932178, 310400972174, 221060379834, 125367239529, 426824249940
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OFFSET
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1,1
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COMMENTS
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Equivalently, a(n) is the least k such that prime(k+1) - prime(k) = prime(k) - prime(k-n). - Giovanni Resta, Apr 03 2017
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LINKS
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FORMULA
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EXAMPLE
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3 is the smallest solution of f(k) = f(k-1); so a(1) = 3. 4 is the smallest solution of f(k) = f(k-1)+f(k-2); so a(2) = 4. 114 is the smallest solution of f(k) = f(k-1)+f(k-2)+f(k-3); so a(3) = 114.
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MATHEMATICA
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a[n_] := Block[{k=n+1}, While[2 Prime[k] != Prime[k + 1] + Prime[k - n], k++]; k]; Array[a, 8] (* Giovanni Resta, Apr 03 2017 *)
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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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