OFFSET
1,1
COMMENTS
Subset of A034708.
LINKS
Paolo P. Lava, Table of n, a(n) for n = 1..1000
EXAMPLE
11: 1/1 + 1/1 = 2;
2441: 1/2 + 1/4 + 1/4 + 1/1 = 2;
3313: 1/3 + 1/3 + 1/1 + 1/3 = 2; etc.
MAPLE
P:=proc(q) local a, k, n, ok;
for n from 1 to q do if isprime(n) then ok:=1; a:=0; for k from 0 to ilog10(n) do
if trunc(n/10^k) mod 10>0 then a:=a+1/(trunc(n/10^k) mod 10) else ok:=0; break; fi; od;
if ok=1 and type(a, integer) then if isprime(a) then print(n) fi; fi; fi; od; end: P(10^9);
# Alternative:
N:= 8: # to get all terms of up to N digits
S1:= proc(t, k, N)
option remember;
if t = 0 then {[]}
elif k = 0 then {}
else
`union`(seq(map(p -> [op(p), k$m], procname(t - m*2520/k, k-1, N-m)),
m = 0 .. min(N, floor(t*k/2520))))
fi
end proc:
targets:= 2520*select(isprime, [$2..N]):
Dlists:= select(p -> convert(p, `+`) mod 3 <> 0, `union`(seq(S1(t, 9, N), t=targets))):
g:= proc(L) local i, m;
m:= nops(L);
op(select(isprime, map(t -> add(t[i]*10^(i-1), i=1..m), combinat:-permute(L))));
end proc:
sort(convert(map(g, Dlists), list)); # Robert Israel, Feb 12 2016
MATHEMATICA
Select[Prime@ Range@ 12000, If[MemberQ[#, 0], False, PrimeQ@ Total[1/#]] &@ IntegerDigits@ # &] (* Michael De Vlieger, Feb 12 2016 *)
PROG
(PARI) isok(n) = if (isprime(n), my(d = digits(n)); vecmin(d) && (denominator(s=sum(k=1, #d, 1/d[k])) == 1) && isprime(s)) \\ Michel Marcus, Feb 12 2016
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava, Feb 12 2016
STATUS
approved