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A261963 Smallest number that can be written as the sum of a Sophie Germain prime (A005384) and a practical number (A005153) in exactly n ways.

%I A261963 #14 Sep 22 2015 08:05:25
%S A261963 2,3,6,23,31,35,65,59,95,131,173,233,203,239,257,299,317,323,473,443,
%T A261963 635,563,671,719,809,701,779,839,803,1109,971,1049,1139,1343,1103,
%U A261963 1409,1433,1607,1481,1499,1559,1523,1769,1679,1643,2069,2063,2309,2111,2141
%N A261963 Smallest number that can be written as the sum of a Sophie Germain prime (A005384) and a practical number (A005153) in exactly n ways.
%e A261963 23 can be written as the sum of a Sophie Germain prime and a practical number in the following three ways: 3 + 20, 5 + 18, 11 + 12.
%e A261963 Since 23 is the smallest number that can be expressed like that in exactly three ways, a(3) = 23.
%o A261963 (PARI) \\ First define the function is_a005153(n) as in A005153
%o A261963 is_a005384(n) = ispseudoprime(n) && ispseudoprime(2*n+1)
%o A261963 count(n) = x=1; y=n-1; i=0; while(y > n/2, if((is_a005153(x) && is_a005384(y)) || (is_a005153(y) && is_a005384(x)), i++); x++; y--); i
%o A261963 a(n) = k=2; while(count(k)!=n, k++); k
%Y A261963 Cf. A005153, A005384, A209253.
%K A261963 nonn
%O A261963 0,1
%A A261963 _Felix Fröhlich_, Sep 06 2015