A269930 Primes whose digits are all prime, sum of digits is prime and sum of reciprocals of digits is also prime.
32233, 32323, 33223, 2222333, 2223233, 2232323, 2233223, 3223223, 272777777, 277727777, 722777777, 772277777, 772777727, 777727277, 777777227, 33333555553, 33355535533, 33355553353, 33533555353, 33553353553, 33553553353, 33553553533, 33555353353, 33555533533, 35335355353, 35335533553, 35353335553
Offset: 1
Examples
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).
Programs
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Maple
P:=proc(q) local a,b, k,ok, ok2, n; 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 a:=0; b:=n; ok2:=1; for k from 1 to ilog10(n)+1 do if isprime(b mod 10) then a:=a+(b mod 10); b:=trunc(b/10); else ok2:=0; break; fi; od; if ok2=1 and isprime(a) then print(n); fi; fi; fi; fi; od; end: P(10^9);
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Mathematica
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 *)
Extensions
More terms from Michael De Vlieger, Mar 08 2016
Comments