A245316 Concatenate n-th composite integer with concatenation of its prime factors in ascending order and the sum of its prime factors.

4224, 6235, 82226, 9336, 10257, 122237, 14279, 15358, 1622228, 182338, 202259, 213710, 2221113, 2422239, 255510, 2621315, 273339, 2822711, 3023510, 322222210, 3331114, 3421719, 355712, 36223310, 3821921, 3931316

Offset

1,1

Links

Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Example

a(2)=6235 since 6=2*3, 2+3=5 and 6 is the second composite integer.

Mathematica

f[n_]:=FactorInteger[n]; con[A_]:=(v1={}; l=Length[A]; Do[v1=Join[v1, IntegerDigits[A[[k]]]], {k, l}]; FromDigits[v1]); alfa[n_]:=(b=f[n]; j=Length[b]; c=Table[Table[b[[k]][[1]], {b[[k]][[2]]}], {k, j}]; w={}; Do[w=Join[w, c[[k]]], {k, j}]; con[w]); omega[n_]:=(b=f[n]; j=Length[b]; c=Table[Table[b[[k]][[1]], {b[[k]][[2]]}], {k, j}]; w={}; Do[w=Join[w, c[[k]]], {k, j}]; Total[w]); nao[n_]:=con[{n, alfa[n], omega[n]}]; v=Select[Range[2, 1000], !PrimeQ[#]&]; Table[nao[v[[k]]], {k, 26}]
compcat[n_]:=Module[{f=Flatten[Table[#[[1]], #[[2]]]&/@FactorInteger[ n]]}, FromDigits[ Join[IntegerDigits[n], Flatten[ IntegerDigits/@ f], IntegerDigits[ Total[f]]]]]; compcat/@Select[Range[40], CompositeQ] (* Harvey P. Dale, Dec 31 2021 *)

Crossrefs

Cf. A002808, A245315.

Sequence in context: A067140 A283725 A109488 * A046335 A046383 A188789

Adjacent sequences: A245313 A245314 A245315 * A245317 A245318 A245319

Keyword

nonn,base

Author

Jahangeer Kholdi, Sep 15 2014

Status

approved