A125689 - OEIS

%I #7 Jan 06 2020 20:32:41

%S 1,10,18,26,31,35,39,80,49,47,57,53,63,59,65,67,248,73,71,79,85,77,93,

%T 105,332,83,89,111,97,482,95,103,101,674,135,129,115,107,800,113,1040,

%U 121,1010,119,127,125,153,159,133,1136,145,131,171,1304,137,151,1520

%N Smallest number having exactly n partitions into three distinct primes.

%C A125688(a(n)) = n and A125688(m) <> n for m < a(n).

%H Andrew Howroyd, <a href="/A125689/b125689.txt">Table of n, a(n) for n = 0..1000</a>

%o (PARI) \\ here b(n) is A125688.

%o b(n, brk=oo)={my(s=0); forprime(p=2, n\3, if((n-p)%2==0, forprime(q=p+1, (n-p)/2-1, if(isprime(n-p-q), s++; if(s>=brk, return(-1))) ))); s}

%o sols(n, lim, f)={my(u=vector(n), r=n); for(i=1, lim, my(t=f(i)); if(t>0 && t<=#u && !u[t], u[t]=i; r--; if(r==0, return(u)))); my(m=1); while(m<=#u && u[m], m++); u[1..m-1]}

%o { my(nn=100); nn++; sols(nn, 10^4, i->b(i, nn)+1) } \\ _Andrew Howroyd_, Jan 06 2020

%Y Cf. A125688.

%K nonn

%O 0,2

%A _Reinhard Zumkeller_, Nov 30 2006

%E Terms a(40) and beyond from _Andrew Howroyd_, Jan 06 2020