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 A239685 Prime numbers for which the sum of reciprocals of nonzero digits equals 1. 0

%I

%S 263,2063,4463,4643,6203,20063,26003,60443,62003,64403,68483,69929,

%T 86843,88463,88643,92699,200063,260003,260999,296099,296909,400643,

%U 406403,406883,446003,449699,460403,464003,464999,468803,488603,494699,496499,496949,499649

%N Prime numbers for which the sum of reciprocals of nonzero digits equals 1.

%C Primes in A214959.

%C Property of the sequence: a(n) == 3 or 9 (mod 10). If n contains nonzero digits, each number > 263 contains at least two identical digits, and the subsequence of the corresponding sum of reciprocals of digits (primes in A037268) is finite.

%e 2063 is in the sequence because 1/2 + 1/6 + 1/3 = 1.

%p with(numtheory):nn:=500000:for m from 1 to nn do:n:=ithprime(m):y:=convert(n,base,10):n2:=nops(y):s:=0:for i from 1 to n2 do: if y[i]<>0 then s:=s+1/y[i]:else fi:od:if s=1 then printf(`%d, `,n):else fi:od:

%t Select[Prime[Range],Total[1/Select[IntegerDigits[#],#!=0&]]==1&] (* _Harvey P. Dale_, May 31 2019 *)

%Y Cf. A037268, A214959.

%K nonn,base

%O 1,1

%A _Michel Lagneau_, Mar 24 2014

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Last modified August 16 20:45 EDT 2022. Contains 356169 sequences. (Running on oeis4.)