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A180007 Number of Goldbach partitions of 6^n. 4
1, 4, 13, 49, 161, 656, 2751, 12505, 58482, 280348, 1374563, 6864809 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Number of ways of writing 6^n as the sum of two odd primes, when the order does not matter. Number of ways writing 6^n as unordered sums of 2 primes. This is to 6 as A006307 is to 2 and as A065577 is to 10. This is the 6th row of the array A[k,n] = Number of ways writing k^n as unordered sums of 2 primes.

A061358(4^n) starts 1, 2, 5, 8, 22, 53, 151, 435, for n=1,2,... (bisection of A006307). A061358(8^n) starts 1, 5, 11, 53, 244, 1314, 7471, (tri-section of A006307). A061358(10^n) = A065577(n). A061358(12^n) = 1, 11, 53, 348, 2523, 20564... A061358(14^n) = 2, 9, 50, 330, 2924, 27225,... - R. J. Mathar, Aug 07 2010

LINKS

Table of n, a(n) for n=1..12.

Manfred Scheucher, Sage Script

FORMULA

a(n) = A061358(6^n) = A061358(A000400(n)).

EXAMPLE

a(1) = 1 because 6^1 = 6 = 3+3.

a(2) = 4 because 6^2 = 36 = 5+31 = 7+29 = 13+23 = 17+19.

a(3) = 13 because 6^3 = 216 = 5+211 = 17+199 = 19+197 = 23+193 = 37+179 = 43+173 = 53+163 = 59+157 = 67+149 = 79+137 = 89+127 = 103+113 = 107+109.

MAPLE

A061358 := proc(n) local a, p ; a := 0 ; p := nextprime(floor((n-1)/2)) ; while p <= n do if isprime(n-p) then a := a+1 ; end if; p := nextprime(p) ; end do ; return a; end proc:

A180007 := proc(n) A061358(6^n) ; end proc:

for n from 1 do printf("%d, \n", A180007(n)) ; end do:

# R. J. Mathar, Aug 07 2010

MATHEMATICA

Table[Count[Sort@ IntegerPartitions[6^n, {2}], {u_, v_} /; And[PrimeQ@ u, u != 2, PrimeQ@ v]], {n, 6}] (* Michael De Vlieger, Jun 02 2015 *)

PROG

(PARI) a(n)=my(t=6^n, s); forprime(p=2, t\2, if(isprime(t-p), s++)); s \\ Charles R Greathouse IV, Jun 02 2015

CROSSREFS

Cf. A000400, A001031, A061358, A065577, A195295.

Sequence in context: A297591 A294298 A300579 * A097948 A096971 A149451

Adjacent sequences:  A180004 A180005 A180006 * A180008 A180009 A180010

KEYWORD

nonn

AUTHOR

Jonathan Vos Post, Aug 06 2010

EXTENSIONS

a(5) corrected, 4 terms added by R. J. Mathar, Aug 07 2010

a(10)-a(12) from Manfred Scheucher, Jun 01 2015

STATUS

approved

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Last modified September 18 21:53 EDT 2020. Contains 337173 sequences. (Running on oeis4.)