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A173688
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Numbers n such that the sum of square of factorial of decimal digits is prime.
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0
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10, 11, 12, 13, 14, 15, 19, 20, 21, 30, 31, 40, 41, 50, 51, 90, 91, 100, 101, 110, 111, 123, 132, 133, 134, 135, 138, 143, 144, 147, 153, 156, 158, 165, 168, 169, 174, 177, 183, 185, 186, 196, 203, 213, 230, 231, 302, 303, 304, 305, 308, 312, 313, 314, 315, 318, 320
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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Let the decimal expansion of n = d(0)d(1)…d(p). Numbers such that sum_{k=0..p}(d(k)!)^2
is prime.
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LINKS
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Table of n, a(n) for n=1..57.
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EXAMPLE
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a(5) =14 is in the sequence because (1!)^2 + (4!)^2 = 1 + 24^2 = 577 and 577
is prime.
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MAPLE
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with(numtheory):for n from 1 to 500 do:l:=length(n):n0:=n:s:=0:for m from 1
to l do:q:=n0:u:=irem(q, 10):v:=iquo(q, 10):n0:=v :s:=s+(u!)^2:od: if type(s, prime)=true
then printf(`%d, `, n):else fi:od:
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MATHEMATICA
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Select[Range[400], PrimeQ[Total[(IntegerDigits[#]!)^2]]&] (* From Harvey P. Dale, Mar 23 2011 *)
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CROSSREFS
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Cf. A165451
Sequence in context: A058946 A118379 A174397 * A008709 A008708 A102490
Adjacent sequences: A173685 A173686 A173687 * A173689 A173690 A173691
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KEYWORD
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nonn,base
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AUTHOR
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Michel Lagneau, Nov 25 2010
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STATUS
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approved
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