A337862 a(n) is the smallest number that can be partitioned into n ways as the sum of two Moran numbers.

0, 36, 63, 174, 198, 306, 312, 399, 1176, 930, 1296, 1989, 1110, 888, 2190, 1896, 2688, 3990, 3630, 3090, 3696, 3810, 8316, 6870, 4710, 12420, 11340, 9180, 13350, 12990, 14070, 14364, 14970, 9900, 15444, 14790, 15012, 18570, 19980, 25164, 23610, 25092, 23790

Offset

0,2

Links

Table of n, a(n) for n=0..42.

Example

0 cannot be written as the sum of two Moran numbers because A001101(1) = 18, so 0 is a term and a(0) = 0.
36 = 18 + 18 = A001101(1) + A001101(1), so a(1) = 36.
63 = 18 + 27 = A001101(1) + A001101(5) and 63 = 21 + 42 = A001101(2) + A001101(4), so a(2) = 63.
174 = 18 + 156 = 21 + 153 = 63 + 111 and 18, 21, 63, 111, 153, 156 are in A001101, so a(3) = 174.
198 = 27 + 171 = 42 + 156 = 45 + 153 = 84 + 114 and 27, 42, 45, 84, 153, 156, 171 are in A001101, so a(4) = 198.

Mathematica

m = 60000; morans = Select[Range[m], PrimeQ[#/Plus @@ IntegerDigits[#]] &]; mx = 43; s = Table[-1, {mx}]; n = 0; c = 0; While[c < mx && n <= m, If[(i = Length[IntegerPartitions[n, {2}, morans]] + 1) <= mx && s[[i]] == -1, c++; s[[i]] = n]; n++]; s (* Amiram Eldar, Oct 21 2020 *)

Prog

(Magma) a:=[]; moran:=func<n|n mod &+Intseq(n) eq 0  and IsPrime( n div &+Intseq(n))>; v:={m:m in [1..40000]|moran(m)}; for n in [0..40] do k:=0; while #RestrictedPartitions(k, 2, v) ne n do k:=k+1; end while; Append(~a, k); end for; a;

Crossrefs

Cf. A001101, A337854, A337861.

Sequence in context: A039419 A043242 A044022 * A082295 A343293 A326666

Adjacent sequences: A337859 A337860 A337861 * A337863 A337864 A337865

Keyword

nonn,base

Author

Marius A. Burtea, Oct 21 2020

Status

approved