cp's OEIS Frontend

A146949 Primes with a prime number of partitions into prime parts.

%I A146949 #17 Dec 06 2020 02:32:20
%S A146949 5,7,17,19,73,103,263,307,653,673,743,823,839,1109,1327,2647,4391,
%T A146949 4621,4967,6389,6661,6829,6871,12227,12269,18839,19861,20663,23497,
%U A146949 23593,23833,24499,25411,28771,29717,36599,40949,41617,46889,47353,49033,50093,50587,50599,51511
%N A146949 Primes with a prime number of partitions into prime parts.
%F A146949 Prime number 7 = 5 + 2 = 3 + 2 + 2, with 3 (prime number) partitions into prime parts. So 7 is in the sequence. Similarly with 17 = 13+2+2 = 11+3+3 = 11+2+2+2 = 7+7+3 = 7+5+5 = 7+5+3+2 = 7+3+3+2+2 = 7+2+2+2+2+2 = 5+5+5+2 = 5+5+3+2+2 = 5+3+3+3+3 = 5+3+3+2+2+2 = 5+2+2+2+2+2+2 = 3+3+3+3+3+2 = 3+3+3+2+2+2+2 = 3+2+2+2+2+2+2+2, having 17 (prime number) partitions into prime parts.
%p A146949 g:=1/(product(1-x^ithprime(j),j=1..500)): gser:= series(g,x=0,3575): a:= proc (n) if isprime(coeff(gser,x,ithprime(n)))=true then ithprime(n) else end if end proc: seq(a(n),n=1..3570); # _Emeric Deutsch_, Nov 09 2008
%p A146949 ##
%p A146949 b:= proc(n, i) local r, m; if n<0 or i<2 then 0 elif n<6 or i<6 then m:= iquo(n, 30, 'r'); (5+15*m+r)*m+ [1, 0, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 5, 6, 7, 7, 8, 9, 9, 11, 11, 12, 13, 14, 15, 16, 17, 18, 19][r+1] else b(n, i):= b(n-i, i) +b(n, prevprime(i)) fi end: a:= proc(n) local k; k:= `if`(n=1, 3, nextprime(a(n-1))); while not (isprime(b(k, k))) do k:= nextprime(k) od; a(n):= k end: seq(a(n), n=1..15);  # _Alois P. Heinz_, Jun 26 2009
%t A146949 jmax = 1000;
%t A146949 pmax = Prime[jmax];
%t A146949 g = 1/Product[1-x^Prime[j], {j, 1, jmax}];
%t A146949 cc = CoefficientList[g + O[x]^pmax, x];
%t A146949 Select[Transpose[{cc, Range[0, Length[cc]-1]}], PrimeQ[#[[1]]] && PrimeQ[#[[2]]]&][[All, 2]] (* _Jean-François Alcover_, Dec 06 2020, after _Emeric Deutsch_ *)
%Y A146949 Cf. A056768.
%K A146949 nonn
%O A146949 1,1
%A A146949 _Lekraj Beedassy_, Nov 03 2008
%E A146949 Edited. - _Lekraj Beedassy_, Nov 08 2008
%E A146949 More terms from _Emeric Deutsch_, Nov 09 2008
%E A146949 a(17) - a(28) from _Alois P. Heinz_, Jun 26 2009
%E A146949 Further terms from _Max Alekseyev_, May 15 2011