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A130007
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Products of two reversible primes that are the reverse of each other such that the products are also the sum of three consecutive primes.
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1
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49, 121, 1207, 22801, 36481, 117907, 863041, 11986939, 32021347, 83148061, 88245211, 106110601, 217297081, 238733401, 242587711, 461772733, 487538353, 606191323, 683819293, 700500007, 758794243, 966634069, 989479087, 995821039, 1117186159, 1205213749, 1208515279
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OFFSET
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1,1
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LINKS
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EXAMPLE
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121 = 11 * 11 = 37 + 41 +43
1207 = 17 * 71 = 397 + 401 + 409
117907 = 157 * 751 = 39293 + 39301 + 39313
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MATHEMATICA
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PrevPrim[n_] := Block[{k = n - 1}, While[ !PrimeQ[k], k-- ]; k]; NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; pal[n_] := FromDigits@ Reverse@ IntegerDigits@n; fQ[n_] := Block[{pn = pal@n, p, q, r, s}, q = PrevPrim[ Ceiling[n*pn/3]]; p = PrevPrim@q; r = NextPrim[ Floor[n*pn/3]]; s = NextPrim@r; n*pn == p + q + r || n*pn == q + r + s]; pd = 6; lst = {}; Do[ pd = NextPrim@pd; If[ PrimeQ@pd && fQ@pd, Print[pd*pal@pd]; AppendTo[lst, pd*pal@pd]], {n, 1000}]; lst = Union@lst (* Robert G. Wilson v, Jun 19 2007 *)
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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Corrected and extended and definition clarified by Chai Wah Wu, Feb 25 2018
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STATUS
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approved
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