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URL: https://oeis.org/A125689

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A125689
a(n) is the smallest number having exactly n partitions into three distinct primes.
3
1, 10, 18, 26, 31, 35, 39, 80, 49, 47, 57, 53, 63, 59, 65, 67, 248, 73, 71, 79, 85, 77, 93, 105, 332, 83, 89, 111, 97, 482, 95, 103, 101, 674, 135, 129, 115, 107, 800, 113, 1040, 121, 1010, 119, 127, 125, 153, 159, 133, 1136, 145, 131, 171, 1304, 137, 151, 1520
OFFSET
0,2
COMMENTS
A125688(a(n)) = n and A125688(m) <> n for m < a(n).
LINKS
MATHEMATICA
nmax = 300; kmax = 10000; c = ConstantArray[Null, nmax];
For[k = 1, k <= kmax, k++,
l = Length@Select[IntegerPartitions[k, {3}, Prime@Range@kmax], #[[1]] > #[[2]] > #[[3]] &];
If[l <= nmax && c[[l]] == Null, c[[l]] = k];
];
Prepend[c[[1 ;; First@FirstPosition[c, Null] - 1]], 1] (* Robert Price, Apr 25 2025 *)
PROG
(PARI) \\ here b(n) is A125688.
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}
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]}
{ my(nn=100); nn++; sols(nn, 10^4, i->b(i, nn)+1) } \\ Andrew Howroyd, Jan 06 2020
CROSSREFS
Cf. A125688.
Sequence in context: A245578 A165250 A257512 * A244573 A230356 A100992
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Nov 30 2006
EXTENSIONS
Terms a(40) and beyond from Andrew Howroyd, Jan 06 2020
STATUS
approved