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

Author

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

Keywords

• nonn
• base

Comments

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

Examples

			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.

Extensions

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