A025583 -id:A025583 - cp's OEIS frontend

A218469 Number of partitions of n into at most three distinct primes (including 1).

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

Offset: 1

Frank M Jackson, Mar 26 2013

nonn

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.

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

T. D. Noe, Table of n, a(n) for n = 1..1000

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

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}]

A309760 Even numbers k such that k-p is composite where p is the largest prime <= k.

Original entry on oeis.org

122, 148, 190, 208, 220, 250, 292, 302, 326, 346, 418, 430, 476, 518, 532, 538, 556, 586, 628, 640, 670, 700, 718, 782, 796, 806, 820, 838, 848, 872, 896, 902, 928, 962, 1006, 1030, 1048, 1060, 1078, 1084, 1138, 1144, 1150, 1162, 1180, 1210, 1246, 1258, 1268, 1274

Offset: 1

Aaron Schäfers, Aug 15 2019

nonn

Cf. A007917, A018252, A049711, A025583.

Select[Range[4, 1274, 2], CompositeQ[# - NextPrime[#, -1]] &] (* Amiram Eldar, Sep 17 2019 *)

is(n) = if(n%2==1 ||n==2, return(0)); my(c = n - precprime(n)); !isprime(c) && c != 1 \\ David A. Corneth, Aug 21 2019

cp's OEIS Frontend

A218469 Number of partitions of n into at most three distinct primes (including 1).

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