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Revision History for A218469

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A218469

Number of partitions of n into at most three distinct primes (including 1).
(history; published version)

#12 by T. D. Noe at Wed Mar 27 14:27:42 EDT 2013

STATUS

editing

approved

#11 by T. D. Noe at Wed Mar 27 14:27:38 EDT 2013

DATA

1, 1, 2, 1, 2, 2, 2, 3, 2, 3, 2, 3, 3, 4, 3, 4, 3, 5, 5, 6, 5, 5, 5, 6, 6, 6, 5, 4, 6, 6, 9, 7, 7, 6, 8, 7, 10, 6, 8, 5, 10, 8, 12, 9, 10, 7, 13, 9, 14, 10, 12, 7, 15, 9, 17, 9, 13, 6, 17, 10, 21, 10, 15, 8, 19, 11, 22, 9, 16, 8, 24, 12, 25, 12, 19, 10, 26, 12, 27, 12, 22, 9

STATUS

approved

editing

#10 by T. D. Noe at Wed Mar 27 14:27:18 EDT 2013

STATUS

editing

approved

#9 by T. D. Noe at Wed Mar 27 14:27:08 EDT 2013

LINKS

T. D. Noe, <a href="/A218469/b218469.txt">Table of n, a(n) for n = 1..1000</a>

EXAMPLE

a(21)=5 as 21 = 2+19 = 1+3+17 = 1+7+13 = 3+5+13 = 3+7+11.

STATUS

proposed

editing

#8 by Frank M Jackson at Tue Mar 26 19:42:21 EDT 2013

STATUS

editing

proposed

Discussion

Wed Mar 27

04:56

Joerg Arndt: After correction this becomes (n>=1)
0, 0, 0, 0, 0, 1, 1, 2, 3, 4, 5, 7, 8, 10, 12, 14, 16, 19, 21, ...
which (dropping some initial terms) is A001399, A069905, and A211540.

09:03

Frank M Jackson: Can you demonstrate your correction with a(21) as an example?
From my perspective, the set of partitions counted in A218469
is a subset of the set of partitions counted in A217008 where
prime multiplicities have been excluded to give the number of
partitions of n with, at most, 3 distinct terms from {1unionPrimes}.
So A217008(21)=9 as 21 = 1+1+19 = 2+19 = 1+3+17 = 2+2+17 = 1+7+13 = 3+5+13 = 3+7+11 = 5+5+11 = 7+7+7 and
A218469(21)=5 as 21 = 2+19 = 1+3+17 = 1+7+13 = 3+5+13 = 3+7+11.
Apologies if I have not understood the point that you are making.

14:22

T. D. Noe: Joerg, this is different because only primes and 1 are in the sums.

#7 by Frank M Jackson at Tue Mar 26 19:40:50 EDT 2013

MATHEMATICA

[parts[[n]]]]][[1]]&&Total[Intersection[parts[[n]]]]==Total[parts[[1]]], count++]; n++]; count); Table[goldbachcount[i], {i, 1, 100}]

[[1]]], count++]; n++]; count); Table[goldbachcount[i], {i, 1, 100}]

#6 by Frank M Jackson at Tue Mar 26 19:38:33 EDT 2013

NAME

Number of partitions of n into at most three disinct distinct primes (including 1).

MATHEMATICA

primeQ[p0_] := If[p0==1, True, PrimeQ[p0]]; SetAttributes[primeQ, Listable]; goldbachcount[p1_] := (parts=IntegerPartitions[p1, 3]; count=0; n=1; While[n<=Length[parts], If[Intersection[Flatten[primeQ[parts[[n]]]]][[1]]&&Total[Intersection[parts[[n]]]]==Total[parts[[1]]], count++]; n++]; count); Table[goldbachcount[i], {i, 1, 100}]

[parts[[n]]]]][[1]]&&Total[Intersection[parts[[n]]]]==Total[parts[[1]]], count++]; n++]; count); Table[goldbachcount[i], {i, 1, 100}]

#5 by Frank M Jackson at Tue Mar 26 19:32:44 EDT 2013

NAME

allocated for Frank M JacksonNumber of partitions of n into at most three disinct primes (including 1).

DATA

OFFSET

1,3

COMMENTS

Using {1 union primes} as the base, the above sequence relies on the strong Goldbach's conjecture that any positive integer is the sum of at most three distinct terms.

EXAMPLE

a(21)=5 as 21 = 2+19 = 1+3+17 = 1+7+13 = 3+5+13 = 3+7+11

MATHEMATICA

CROSSREFS

Cf. A002375, A025583, A068307, A071335, A185101, A218007.

KEYWORD

allocated

nonn

AUTHOR

Frank M Jackson, Mar 26 2013

STATUS

approved

editing

#4 by Frank M Jackson at Tue Mar 26 19:32:44 EDT 2013

NAME

allocated for Frank M Jackson

KEYWORD

recycled

allocated

#3 by R. J. Mathar at Sun Mar 10 16:26:08 EDT 2013

STATUS

editing

approved