A358671 Numbers k such that for all factorizations of k as x*y, the sum x+y is carryfree when the addition is done in the primorial base, A049345.

2, 4, 6, 14, 18, 24, 26, 28, 38, 42, 52, 54, 62, 72, 74, 76, 78, 86, 96, 98, 114, 122, 124, 126, 134, 146, 148, 158, 172, 186, 194, 206, 218, 222, 244, 254, 258, 268, 278, 292, 302, 314, 316, 326, 362, 366, 386, 388, 398, 402, 412, 422, 434, 436, 438, 446, 458, 474, 482, 508, 518, 542, 554, 556, 558

Offset: 1

Author

Antti Karttunen, Nov 26 2022

Keywords

• nonn
• base

Comments

Numbers k such that there are no factorization of k into such a pair of natural numbers x and y that would generate any carries when added together in the primorial base.

Examples

			8 is not included, because while factorization 1*8 would yield a carry-free sum ("1" and "110" added together gives "111" = 9 in primorial base, A049345), factorization 2*4 would not, as 2+4 (= "10" + "20") and 2 is the max. allowed digit in the second rightmost place.
		

Links

• Index entries for sequences related to primorial base

Crossrefs

Cf. A038548, A049345, A276086, A329041, A358233, A358670 (characteristic function).

Cf. also A358673.

Programs

PARI

isA358671(n) = A358670(n);

Formula

{k | A358233(k) = A038548(k)}.