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A146949 Primes with a prime number of partitions into prime parts. 0
5, 7, 17, 19, 73, 103, 263, 307, 653, 673, 743, 823, 839, 1109, 1327, 2647, 4391, 4621, 4967, 6389, 6661, 6829, 6871, 12227, 12269, 18839, 19861, 20663, 23497, 23593, 23833, 24499, 25411, 28771, 29717, 36599, 40949, 41617, 46889, 47353, 49033, 50093, 50587, 50599, 51511 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
FORMULA
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.
MAPLE
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
##
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
MATHEMATICA
jmax = 1000;
pmax = Prime[jmax];
g = 1/Product[1-x^Prime[j], {j, 1, jmax}];
cc = CoefficientList[g + O[x]^pmax, x];
Select[Transpose[{cc, Range[0, Length[cc]-1]}], PrimeQ[#[[1]]] && PrimeQ[#[[2]]]&][[All, 2]] (* Jean-François Alcover, Dec 06 2020, after Emeric Deutsch *)
CROSSREFS
Cf. A056768.
Sequence in context: A023519 A023517 A128491 * A048700 A331892 A331893
KEYWORD
nonn
AUTHOR
Lekraj Beedassy, Nov 03 2008
EXTENSIONS
Edited. - Lekraj Beedassy, Nov 08 2008
More terms from Emeric Deutsch, Nov 09 2008
a(17) - a(28) from Alois P. Heinz, Jun 26 2009
Further terms from Max Alekseyev, May 15 2011
STATUS
approved

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Last modified February 29 20:48 EST 2024. Contains 370428 sequences. (Running on oeis4.)