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Largest n-digit prime with digit sum n, or 0 if no such prime exists.
2

%I #7 Dec 11 2024 05:42:12

%S 0,11,0,3001,30011,0,5001001,61000001,0,9000000001,82000000001,0,

%T 9210000000001,92200000000001,0,9500000100000001,97000000000000001,0,

%U 9800000000000010001,98010000010000000001,0,9920000010000000000001,99300010000000000000001,0,9950000010000000000000001

%N Largest n-digit prime with digit sum n, or 0 if no such prime exists.

%H Andrew Howroyd, <a href="/A073865/b073865.txt">Table of n, a(n) for n = 1..500</a>

%o (PARI)

%o a(n)={

%o my(recurse(k,r,p)=if(k==1, if(r<=9 && isprime(p+r), p+r, 0),

%o my(t=0,c=min(r-1,9));

%o while(!t&&c>=0, t=self()(k-1, r-c, (p+c)*10); c--); t)) ;

%o my(t=0, c=min(n,9)); if(n%3, while(!t&&c>0, t=recurse(n-1, n-c, c*10); c--)); t

%o } \\ _Andrew Howroyd_, Dec 10 2024

%Y Cf. A073864.

%K base,nonn

%O 1,2

%A _Amarnath Murthy_, Aug 15 2002

%E a(7) onwards from _Andrew Howroyd_, Dec 10 2024