A388280 Numbers k for which the sum of k and sigma(k)-k does not generate any carries when done in the primorial base (A049345).

1, 2, 6, 8, 12, 30, 32, 49, 60, 66, 72, 78, 98, 120, 121, 150, 210, 228, 240, 242, 246, 258, 270, 338, 361, 364, 420, 426, 438, 441, 450, 462, 498, 512, 558, 570, 600, 618, 630, 636, 660, 678, 722, 726, 738, 750, 756, 841, 846, 870, 906, 930, 948, 961, 966, 1038, 1058, 1080, 1086, 1146, 1260, 1320, 1350, 1369, 1386

Offset

1,2

Comments

Apparently, the asymptotic density of this sequence is 0. - Amiram Eldar, Sep 18 2025

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Amiram Eldar, Plot of Sum_{k=1..n} a(k) / ((1/2)*a(n)^2) vs. n for n = 10^2..10^6.

Index entries for sequences related to primorial base.

Index entries for sequences related to sigma(n).

Formula

{k | A329041(k, A001065(k)) = 1}.

{k | A388281(k) = 0}.

Example

For k = 8, A001065(8) = 7, A000203(8) = 15 (= 8+7), and A049345(8) = 110, A049345(7) = 101, thus they sum cleanly without carries (in primorial base) to A049345(15) = 211, therefore 8 is included as a term.
For k = 750, A001065(750) = 1122, A000203(750) = 1872 (= 750 + 1122), and A049345(750) = 34000 while A049345(1122) = 52200, and they sum cleanly without carries (in primorial base) to A049345(1872) = 86200, therefore 750 is included as a term.

Prog

(PARI)
no_carries_in_primorial_base(x, y) = { my(p=2); while(x && y, if(((x%p)+(y%p)) >= p, return(0)); x \= p; y \= p; p = nextprime(1+p)); (1); };
is_A388280(n) = no_carries_in_primorial_base(n, sigma(n)-n);

Crossrefs

Positions of 0's in A388281.

Cf. A000203, A001065, A049345, A276086, A329041, A379493, A388031.

Sequence in context: A346587 A226818 A113462 * A065392 A030457 A296300

Adjacent sequences: A388277 A388278 A388279 * A388281 A388282 A388283

Keyword

nonn,base

Author

Antti Karttunen, Sep 16 2025

Status

approved