A370137 Sums of three primorials > 1.

6, 10, 14, 18, 34, 38, 42, 62, 66, 90, 214, 218, 222, 242, 246, 270, 422, 426, 450, 630, 2314, 2318, 2322, 2342, 2346, 2370, 2522, 2526, 2550, 2730, 4622, 4626, 4650, 4830, 6930, 30034, 30038, 30042, 30062, 30066, 30090, 30242, 30246, 30270, 30450, 32342, 32346, 32370, 32550, 34650, 60062, 60066, 60090, 60270, 62370, 90090

Offset: 1

Author

Antti Karttunen, Mar 09 2024

Keywords

• nonn

Examples

			6 = A002110(1) + A002110(1) + A002110(1) = 2+2+2.
10 = A002110(2) + A002110(1) + A002110(1) = 6+2+2.
14 = A002110(2) + A002110(2) + A002110(1) = 6+6+2.
18 = A002110(2) + A002110(2) + A002110(2) = 6+6+6.
38 = A002110(3) + A002110(2) + A002110(1) = 30+6+2.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..15180
• Index entries for sequences related to primorial numbers

Crossrefs

Cf. A000292, A002110, A276086, A276150, A369979, A370138.

Subsequence of A370133.

Cf. also A370134.

Programs

Mathematica

nn = 6; MapIndexed[Set[P[First[#2] - 1], #1] &, FoldList[Times, 1, Prime@ Range[nn]]]; Table[P[i] + P[j] + P[k], {i, nn}, {j, i}, {k, j}] // Flatten (* Michael De Vlieger, Mar 09 2024 *)

PARI

up_to = 15180;
A002110(n) = prod(i=1,n,prime(i));
A370137list(up_to) = { my(v = vector(up_to), i=0); for(x=1,oo, for(y=1,x, for(z=1,y, i++; if(i > up_to, return(v)); v[i] = A002110(x)+A002110(y)+A002110(z)))); (v); };
v370137 = A370137list(up_to);
A370137(n) = v370137[n];

Formula

For n > 1, A276150(a(n)) = 3.

For n > 1, A276086(a(n)) = A369979(n).