A249447 Least n-digit prime whose digit sum is also prime.

2, 11, 101, 1013, 10037, 100019, 1000033, 10000019, 100000037, 1000000033, 10000000019, 100000000019, 1000000000039, 10000000000037, 100000000000031, 1000000000000037, 10000000000000079, 100000000000000013, 1000000000000000031, 10000000000000000051, 100000000000000000039

Offset

1,1

Comments

Subsequence of A046704 (primes with digits sum being prime).

Some terms of this sequence are also in A003617, the least n-digit primes. - Michel Marcus, Oct 30 2014

Links

Paolo P. Lava, Table of n, a(n) for n = 1..100

Example

a(1) = 2 because it is the least prime with just one digit.
a(2) = 11 because it is the least prime with 2 digits whose sum, 1 + 1 = 2, is a prime.
Again, a(7) = 1000033 because it is the least prime with 7 digits whose sum is a prime: 1 + 0 + 0 + 0 + 0 + 3 + 3 = 7.

Maple

P:=proc(q) local a, b, k, n; for k from 0 to q do
for n from 10^k to 10^(k+1)-1 do if isprime(n) then a:=n; b:=0;
while a>0 do b:=b+(a mod 10); a:=trunc(a/10); od;
if isprime(b) then print(n); break; fi; fi;
od; od; end: P(10^3);

Prog

(PARI) a(n) = {p = nextprime(10^(n-1)); while (!isprime(sumdigits(p)), p = nextprime(p+1)); p; } \\ Michel Marcus, Oct 29 2014

Crossrefs

Cf. A003617, A046704, A068166, A249448.

Sequence in context: A003617 A114018 A089770 * A199302 A069663 A241100

Adjacent sequences: A249444 A249445 A249446 * A249448 A249449 A249450

Keyword

nonn,base

Author

Paolo P. Lava, Oct 29 2014

Status

approved