A373599 Numbers k such that k and A327860(k) are both multiples of 3, where A327860 is the arithmetic derivative of the primorial base exp-function.

0, 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, 198, 222, 240, 258, 276, 294, 312, 330, 348, 366, 384, 402, 426, 444, 462, 480, 498, 516, 534, 552, 570, 588, 606, 624, 630, 648, 666, 684, 702, 720, 738, 756, 774, 792, 810, 828, 852, 870, 888, 906, 924, 942, 960, 978, 996, 1014, 1032, 1056, 1074, 1092, 1110, 1128

Offset: 1

Author

Antti Karttunen, Jun 18 2024

Keywords

• nonn

Comments

If x and y are terms and if A329041(x,y) = 1 (i.e., when adding x and y together will not generate any carries in the primorial base), then x+y is also a term. This follows from the quasi-exponential nature of A276086 and because A373144 is a multiplicative semigroup.

Examples

			18 = 3*6 is included, because also A327860(18) = 75 is a multiple of 3.
222 = 3*74 is included, because also A327860(222) = 135 is a multiple of 3.
240 = 3*80 is included, because also A327860(240) = 18 is a multiple of 3.
258 = 3*86 is included, because also A327860(258) = 8025 is a multiple of 3. Note that A049345(18) = 300, A049345(240) = 11000, and A049345(240+18) = 11300, so the sum in this case is carry-free (cf. the comment).
2556 = 3*852 is included, because also A327860(2556) = 2556 is a multiple of 3 (see also A328110 and A373144).
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20020
• Index entries for sequences related to primorial base

Crossrefs

Cf. A049345, A276086, A327860, A329041, A373598 (characteristic function).

Indices of multiples of 3 in A351083.

Intersection of A008585 and A369654.

Differs from A008600 (multiples of 18) for the first time at a(13) = 222, which is not a multiple of 18.

Cf. also A373144.

Programs

PARI

isA373599 = A373598;