cp's OEIS Frontend

A263448 Primes that can be expressed as a sum of primes where no digit appears more than once.

%I A263448 #41 Jan 07 2018 08:36:34
%S A263448 5,7,41,47,61,67,89,103,401,809
%N A263448 Primes that can be expressed as a sum of primes where no digit appears more than once.
%C A263448 This sequence is finite because if n has more than 5 digits then any sum of positive integers adding up to n will have more than 5 digits, forcing some digit to repeat. The last term is a(10) = 809. - _Charles R Greathouse IV_, Nov 10 2016
%e A263448 a(1) = 5 = 2 + 3.
%e A263448 a(2) = 7 = 2 + 5.
%e A263448 a(3) = 41 = 5 + 7 + 29.
%e A263448 a(4) = 47 = 5 + 13 + 29.
%e A263448 a(5) = 61 = 2 + 59.
%e A263448 a(6) = 67 = 5 + 19 + 43.
%e A263448 a(7) = 89 = 5 + 23 + 61.
%e A263448 a(8) = 103 = 2 + 5 + 7 + 89.
%e A263448 a(9) = 401 = 5 + 7 + 389.
%e A263448 a(10) = 809 = 5 + 43 + 761.
%o A263448 (PARI) has(n,v,start=2)=my(d=digits(n),s=Set(d)); if(#d==#s && isprime(n) && #setintersect(s,v)==#s, return(1)); forprime(p=start,n\2, s=Set(d=digits(p)); if(#s==#d && #setintersect(s,v)==#s && has(n-p, setminus(v,s),p+1), return(1))); 0
%o A263448 is(n)=my(d=digits(n),s=Set(d)); #d==#s && isprime(n) && has(n, setminus([0..9],s)) \\ _Charles R Greathouse IV_, Nov 10 2016
%Y A263448 Cf. A010784.
%K A263448 base,nonn,fini,full
%O A263448 1,1
%A A263448 _José de Jesús Camacho Medina_, Nov 09 2016
%E A263448 a(4), a(6), a(7), a(9), and a(10) from _Charles R Greathouse IV_, Nov 10 2016