A339215 Primorial-base self numbers: numbers not of the form k + A276150(k).

1, 4, 11, 18, 25, 32, 35, 42, 49, 56, 63, 66, 73, 80, 87, 94, 97, 104, 111, 118, 125, 128, 135, 142, 149, 156, 159, 166, 173, 180, 187, 190, 197, 204, 229, 236, 243, 246, 253, 260, 267, 274, 277, 284, 291, 298, 305, 308, 315, 322, 329, 336, 339, 346, 353, 360

Offset: 1

Author

Amiram Eldar, Nov 27 2020

Keywords

• nonn
• base

Comments

Analogous to self numbers (A003052) using primorial base representation (A049345) instead of decimal expansion.

The numbers of terms that do not exceed 10^k, for k = 0, 1, ..., are 1, 2, 17, 150, 1469, 14669, 146680, 1466723, 14667162, 146671527, 1466715137, ... . Apparently, the asymptotic density of this sequence exists and equals 0.1466715... . - Amiram Eldar, Aug 08 2025

References

• József Sándor and Borislav Crstici, Handbook of Number theory II, Kluwer Academic Publishers, 2004, Chapter 4, pp. 384-386.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Self Number.
• Wikipedia, Primorial number system.
• Wikipedia, Self number.
• Index entries for Colombian or self numbers and related sequences

Crossrefs

Cf. A003052, A010061, A010064, A010067, A010070, A049345, A276150, A333426, A339211, A339212, A339213, A339214.

Programs

Mathematica

max = 4; bases = Prime@Range[max, 1, -1]; m = Times @@ bases; s[n_] := n + Plus @@ IntegerDigits[n, MixedRadix[bases]]; Complement[Range[m], Array[s, m]]