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A282971 Number of compositions (ordered partitions) of n into primes of form x^2 + y^2 (A002313). 1

%I

%S 1,0,1,0,1,1,1,2,1,3,2,4,4,6,7,9,11,15,18,24,29,37,48,58,78,92,124,

%T 149,195,243,308,393,490,629,786,1004,1263,1603,2024,2564,3239,4106,

%U 5184,6571,8301,10508,13298,16807,21296,26895,34082,43060,54528,68952,87245,110392,139622,176696,223484,282798,357731

%N Number of compositions (ordered partitions) of n into primes of form x^2 + y^2 (A002313).

%C Number of compositions (ordered partitions) of n into primes congruent to 1 or 2 mod 4.

%C Conjecture: every number > 16 is the sum of at most 4 primes of form x^2 + y^2.

%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>

%F G.f.: 1/(1 - Sum_{k>=1} x^A002313(k)).

%e a(12) = 4 because we have [5, 5, 2], [5, 2, 5], [2, 2, 5] and [2, 2, 2, 2, 2, 2].

%t nmax = 60; CoefficientList[Series[1/(1 - Sum[Boole[SquaresR[2, k] != 0 && PrimeQ[k]] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]

%o (PARI) Vec(1/(1 - sum(k=1, 60, (isprime(k) && k%4<3)*x^k)) + O(x^61)) \\ _Indranil Ghosh_, Mar 15 2017

%Y Cf. A002124, A002313, A023360, A077608, A280917, A282906, A282970.

%K nonn

%O 0,8

%A _Ilya Gutkovskiy_, Feb 25 2017

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Last modified October 22 04:29 EDT 2018. Contains 316431 sequences. (Running on oeis4.)