A372055 For a positive number k, let L(k) denote the list consisting of k followed by the prime factors of k, with repetition, in nondecreasing order; sequence gives k such that the digits of L(k) are in nondecreasing order.

1, 2, 3, 5, 7, 11, 12, 25, 35, 111, 112, 125, 222, 245, 333, 335, 445, 1225, 2225, 11125, 33445, 334445, 3333335, 3334445, 3444445, 33333445, 333333335, 334444445, 3333333335, 33333334445, 333333333335, 33333333334445, 33333333444445, 444444444444445, 2222222222222225

Offset

1,2

Comments

This is the union of {1,2,3,5,7}, A004022, and A372029.

Links

Table of n, a(n) for n=1..35.

Example

L(1) = [1], L[2] = [2,2], L[11] = [11,11], L[12] = [12,2,2,3}.
See A372029 for further examples.
The prime k = 1111111111111111111 = A004022(2) will eventually be a term, since L(1111111111111111111) = [1111111111111111111,1111111111111111111], which certainly has digits in nondecreasing order.

Crossrefs

Cf. A004022, A372029.

Sequence in context: A205667 A241506 A361851 * A165132 A193063 A039715

Adjacent sequences: A372052 A372053 A372054 * A372056 A372057 A372058

Keyword

nonn,base

Author

Scott R. Shannon and N. J. A. Sloane, Apr 22 2024

Extensions

More terms from Michael S. Branicky, Apr 23 2024 using A004022 and A372029.

Status

approved