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

1,1

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.

Links

Table of n, a(n) for n=1..35.

Example

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

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 *)

Crossrefs

Cf. A037268, A214959.

Sequence in context: A023314 A054802 A369877 * A108823 A229480 A266036

Adjacent sequences: A239682 A239683 A239684 * A239686 A239687 A239688

Keyword

nonn,base

Author

Michel Lagneau, Mar 24 2014

Status

approved