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A249448
Largest n-digit prime whose digit sum is also prime.
3
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
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
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava, Oct 29 2014
STATUS
approved