A249448 Largest n-digit prime whose digit sum is also prime.

7, 89, 991, 9967, 99991, 999983, 9999971, 99999989, 999999937, 9999999943, 99999999821, 999999999989, 9999999999971, 99999999999923, 999999999999883, 9999999999999851, 99999999999999997, 999999999999999967, 9999999999999999919, 99999999999999999989, 999999999999999999829

Offset

1,1

Comments

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

Some terms of this sequence are also in A003618, the largest n-digit primes.

Links

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

Example

a(1) = 7 because it is the largest prime with just one digit.
a(2) = 89 because it is the largest prime with 2 digits whose sum, 8 + 9 = 17, is a prime.
Again, a(7) = 9999971 because it is the largest prime with 7 digits whose sum is a prime: 9 + 9 + 9 + 9 + 9 + 7 + 1 = 53.

Maple

P:=proc(q) local a, b, k, n; for k from 0 to q do
for n from 10^(k+1)-1 by -1 to 10^k 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);

Mathematica

Table[Module[{p=NextPrime[10^n, -1]}, While[!PrimeQ[Total[IntegerDigits[p]]], p=NextPrime[p, -1]]; p], {n, 25}] (* Harvey P. Dale, Jun 20 2023 *)

Prog

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

Crossrefs

Cf. A046704, A103545, A249447.

Sequence in context: A121044 A107109 A089771 * A069661 A069662 A359646

Adjacent sequences: A249445 A249446 A249447 * A249449 A249450 A249451

Keyword

nonn,base

Author

Paolo P. Lava, Oct 29 2014

Status

approved