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A214844 Number of partitions of 2^n into three distinct primes. 0
0, 0, 0, 1, 3, 2, 10, 8, 32, 18, 75, 51, 292, 140, 518, 534, 2167, 1292, 6055, 4318, 23899, 16589, 53108, 46683, 312340, 159483, 567857, 639256, 2810965, 1826974 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

Table of n, a(n) for n=1..30.

Index entries for sequences related to Goldbach conjecture

FORMULA

a(n) = A061357(2^(n-1) - 1) for n > 2. - Charles R Greathouse IV, Mar 08 2013

EXAMPLE

a(4) = 1 because 2^4 = 16 = 2 + 3 + 11 (1 partition),

a(5) = 3 because 2^5 = 32 = 2 + 7 + 23 = 2 + 11 + 19 = 2 + 13 + 17 (3 partitions).

MATHEMATICA

Do[Print[{k, n=2^k; s=0; Do[p=Prime[i]; Do[q=Prime[j]; r=n-p-q; If[r>q && PrimeQ[r], s++], {j, i+1, PrimePi[(n-p)/2]}], {i, 1}]; s}], {k, 30}]

Table[m = 2^n - 2; cnt = 0; p = 3; While[p < m/2, If[PrimeQ[m - p], cnt++]; p = NextPrime[p]]; cnt, {n, 20}] (* T. D. Noe, Mar 08 2013 *)

PROG

(PARI) a(n)=my(N=2^n-2, s); forprime(p=3, N/2-1, s+=ispseudoprime(N-p)); s \\ Charles R Greathouse IV, Mar 08 2013

CROSSREFS

Cf. A125688.

Sequence in context: A268531 A056861 A302846 * A214966 A103245 A019242

Adjacent sequences:  A214841 A214842 A214843 * A214845 A214846 A214847

KEYWORD

nonn

AUTHOR

Zak Seidov, Mar 08 2013

STATUS

approved

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Last modified May 21 22:24 EDT 2019. Contains 323467 sequences. (Running on oeis4.)