A344512 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A344512

a(n) is the least number larger than 1 which is a self number in all the bases 2 <= b <= n.

4, 13, 13, 13, 287, 287, 2971, 2971, 27163, 27163, 90163, 90163, 5940609, 5940609, 6069129, 6069129, 276404649, 276404649

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,1

COMMENTS

Since the sequence of base-b self numbers for odd b is the sequence of the odd numbers (A005408) (Joshi, 1973), all the terms beyond a(2) are odd numbers.

For the corresponding sequence with only even bases, see A344513.

a(20) > 1.5*10^10, if it exists.

REFERENCES

Vijayshankar Shivshankar Joshi, Contributions to the theory of power-free integers and self-numbers, Ph.D. dissertation, Gujarat University, Ahmedabad (India), October, 1973.

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

LINKS

Table of n, a(n) for n=2..19.

Eric Weisstein's World of Mathematics, Self Number.

Wikipedia, Self number.

Index entries for Colombian or self numbers and related sequences

FORMULA

a(2*n+1) = a(2*n) for n >= 2.

EXAMPLE

a(2) = 4 since the least binary self number after 1 is A010061(2) = 4.

a(3) = 13 since the least binary self number after 1 which is also a self number in base 3 is A010061(4) = 13.

MATHEMATICA

s[n_, b_] := n + Plus @@ IntegerDigits[n, b]; selfQ[n_, b_] := AllTrue[Range[n, n - (b - 1) * Ceiling @ Log[b, n], -1], s[#, b] != n &]; a[2] = 4; a[b_] := a[b] = Module[{n = a[b - 1]}, While[! AllTrue[Range[2, b], selfQ[n, #] &], n++]; n]; Array[a, 10, 2]

CROSSREFS

Cf. A003052, A010061, A010064, A010067, A010070, A339211, A339212, A339213, A339214, A339215, A342729, A344513.

Similar sequences: A016038, A217705, A225427, A226320, A228768, A258107.

Sequence in context: A287895 A050223 A301792 * A168401 A370644 A081738

Adjacent sequences: A344509 A344510 A344511 * A344513 A344514 A344515

KEYWORD

nonn,base,more

AUTHOR

Amiram Eldar, May 21 2021

STATUS

approved