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A046713
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Multiplicative and additive primes: primes where the product and sum of digits are also prime.
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6
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2, 3, 5, 7, 113, 131, 151, 311, 2111, 11113, 11117, 11131, 11171, 11311, 111121, 111211, 112111, 1111151, 1111711, 1117111, 1171111, 111111113, 111111131, 111113111, 115111111, 131111111, 1111111121, 1111211111, 1121111111, 11111111113, 11111111131, 11113111111
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OFFSET
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1,1
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COMMENTS
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Any term of this sequence has one prime digit and all other digits are 1. - Sean A. Irvine, Apr 17 2021
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LINKS
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MATHEMATICA
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d[n_]:=IntegerDigits[n]; t={}; Do[p=Prime[n]; If[PrimeQ[Plus@@(x=d[p])]&&PrimeQ[Times@@x], AppendTo[t, p]], {n, 2*10^5}]; t (* Jayanta Basu, May 18 2013 *)
Select[Prime[Range[5033*10^5]], AllTrue[{Total[IntegerDigits[ #]], Times@@ IntegerDigits[ #]}, PrimeQ]&] (* or -- much faster *) Select[Union[ Flatten[ Table[FromDigits/@Permutations[PadRight[{p}, n, 1]], {p, {2, 3, 5, 7}}, {n, 11}]]], AllTrue[{#, Total[ IntegerDigits[#]], Times@@ IntegerDigits[ #]}, PrimeQ]&] (* Harvey P. Dale, Feb 28 2022 *)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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