cp's OEIS Frontend

A269930 Primes whose digits are all prime, sum of digits is prime and sum of reciprocals of digits is also prime.

%I A269930 #21 Jun 26 2019 00:39:33
%S A269930 32233,32323,33223,2222333,2223233,2232323,2233223,3223223,272777777,
%T A269930 277727777,722777777,772277777,772777727,777727277,777777227,
%U A269930 33333555553,33355535533,33355553353,33533555353,33553353553,33553553353,33553553533,33555353353,33555533533,35335355353,35335533553,35353335553
%N A269930 Primes whose digits are all prime, sum of digits is prime and sum of reciprocals of digits is also prime.
%C A269930 Intersection of A019546, A046704, A266815.
%C A269930 Furthermore, 32233, 32323 and 2223233 are primes with prime subscripts (A006450). In fact, 32233 is the 3457th prime, 32323 is the 3467th prime, and 2223233 is the 164239th prime.
%e A269930 32233 is prime, its digits are primes (2 and 3), their sum is prime (3 + 2 + 2 + 3 + 3 = 13) and the sum of reciprocal of digits is also prime (1/3 + 1/2 + 1/2 + 1/3 + 1/3 = 2).
%p A269930 P:=proc(q) local a,b, k,ok, ok2, n;
%p A269930 for n from 1 to q do if isprime(n) then ok:=1; a:=0; for k from 0 to ilog10(n) do
%p A269930 if trunc(n/10^k) mod 10>0 then a:=a+1/(trunc(n/10^k) mod 10) else ok:=0; break; fi; od;
%p A269930 if ok=1 and type(a,integer) then if isprime(a) then a:=0; b:=n; ok2:=1;
%p A269930 for k from 1 to ilog10(n)+1 do if isprime(b mod 10) then a:=a+(b mod 10); b:=trunc(b/10);
%p A269930 else ok2:=0; break; fi; od; if ok2=1 and isprime(a) then print(n); fi; fi; fi; fi; od; end: P(10^9);
%t A269930 Select[Select[Flatten@ Map[Map[FromDigits, Tuples[{2, 3, 5, 7}, #]] &, Range@ 11], PrimeQ], And[PrimeQ[Total@ #], PrimeQ[Total[1/#]]] &@ IntegerDigits@ # &] (* _Michael De Vlieger_, Mar 08 2016 *)
%Y A269930 Cf. A000040, A006450, A019546, A046704, A266815.
%K A269930 nonn,easy,base
%O A269930 1,1
%A A269930 _Paolo P. Lava_, Mar 08 2016
%E A269930 More terms from _Michael De Vlieger_, Mar 08 2016