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

1,1

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.

Links

Table of n, a(n) for n=1..65.

Index entries for sequences related to primorial base

Formula

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

Example

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.

Prog

(PARI) isA358671(n) = A358670(n);

Crossrefs

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

Cf. also A358673.

Sequence in context: A138307 A323101 A124693 * A095698 A277909 A064409

Adjacent sequences: A358668 A358669 A358670 * A358672 A358673 A358674

Keyword

nonn,base

Author

Antti Karttunen, Nov 26 2022

Status

approved