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%I #29 Apr 20 2019 03:01:55
%S 1,0,0,1,0,0,0,1,0,0,1,1,0,0,1,0,0,0,1,1,0,1,1,1,0,0,2,0,0,1,2,1,0,2,
%T 2,0,0,2,1,0,1,2,2,1,1,2,1,1,0,2,3,0,2,3,3,0,1,4,1,1,2,4,2,1,3,3,3,1,
%U 3,4,3,2,2,6,3,1,4,6,4,1,6,6,3,3,5,7,3,3,6,7,6,2,7,9,3,2,7,10,2,4,11,10,4,5,12,7
%N Number of partitions of n into distinct primes of the form 4k + 3.
%C a(0) = 1 corresponds to the empty partition {}.
%H Alois P. Heinz, <a href="/A024942/b024942.txt">Table of n, a(n) for n = 0..10000</a>
%e a(26) = 2 since 26 = 3 + 23 = 7 + 19.
%e Even though 27 = (3 * 3) + 7 + 11 = (2 * 3) + (3 * 7) = (9 * 3), there is no partition of 27 into primes of the form 4k - 1 with all parts distinct. Hence a(27) = 0.
%t searchMax = 108; primes4km1 = Select[4Range[Ceiling[searchMax/4]] - 1, PrimeQ]; Table[Length[Select[IntegerPartitions[n, All, primes4km1], DuplicateFreeQ]], {n, 0, searchMax}] (* _Alonso del Arte_, Apr 16 2019 *)
%o (PARI) { my(V=select(x->x%4==3,primes(40))); my(x='x+O('x^V[#V])); Vec(prod(k=1,#V,1+x^V[k])) } \\ _Joerg Arndt_, Apr 19 2019
%Y Cf. A024941 (4k + 1).
%K nonn
%O 0,27
%A _Clark Kimberling_
%E Definition clarified by _Felix Fröhlich_, Apr 17 2019
%E a(0) = 1 prepended by _Joerg Arndt_, Apr 19 2019
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