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

263, 2063, 4463, 4643, 6203, 20063, 26003, 60443, 62003, 64403, 68483, 69929, 86843, 88463, 88643, 92699, 200063, 260003, 260999, 296099, 296909, 400643, 406403, 406883, 446003, 449699, 460403, 464003, 464999, 468803, 488603, 494699, 496499, 496949, 499649

Offset: 1

Author

Michel Lagneau, Mar 24 2014

Keywords

• nonn
• base

Comments

Primes in A214959.

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.

Examples

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

Crossrefs

Cf. A037268, A214959.

Programs

Maple

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:

Mathematica

Select[Prime[Range[42000]],Total[1/Select[IntegerDigits[#],#!=0&]]==1&] (* Harvey P. Dale, May 31 2019 *)