A350061 Numbers k for which there exists a preimage m_1 such that A349194(m_1) = k but there is no preimage m_2 such that A349278(m_2) = k.

25, 49, 75, 125, 147, 242, 245, 343, 363, 375, 484, 605, 625, 676, 726, 845, 847, 968, 1014, 1029, 1089, 1183, 1210, 1225, 1352, 1452, 1521, 1690, 1694, 1715, 1815, 1875, 1936, 2028, 2178, 2312, 2366, 2401, 2420, 2535, 2541, 2601, 2662, 2704, 2890, 3025, 3042, 3125, 3267, 3380

Offset: 1

Author

Bernard Schott, Dec 12 2021

Keywords

• nonn
• more
• base

Comments

Numbers that can be expressed as the product of the sum of the first i digits of k, as i goes from 1 to the total number of digits of k for some k, but not as the product of the sum of the last i digits of m, with i going from 1 to the total number of digits of m, for any m.

The preimages m_1 are necessarily multiples of 10; the first few are 50, 70, 320, 500, 340, ...

As A349733 is a subsequence of A349865, there are no numbers t for which there exists a preimage m_4 such that A349278(m_4) = t but there is no preimage m_3 such that A349194(m_3) = t.

Examples

			A349194(122) = 1*(1+2)*(1+2+2) = 15 and A349278(23) = 3*(3+2) = 15, hence, 15 is not a term.
A349194(50) = 5*(5+0) = 25 but there is no m_2 such that A349278(m_2) = 25, because 25 = A349865(1), hence 25 is a term.
A349194(340) = 3*(3+4)*(3+4+0) = 147 but there is no m_2 such that A349278(m_2) = 340, because 147 = A349865(47), hence 147 is a term.
		

Crossrefs

Cf. A349194, A349278.

Equals A349865 \ A349733.

Extensions

a(6)-a(50) from Michel Marcus, Dec 12 2021