A350061 - OEIS

%I #25 Dec 17 2021 20:40:04

%S 25,49,75,125,147,242,245,343,363,375,484,605,625,676,726,845,847,968,

%T 1014,1029,1089,1183,1210,1225,1352,1452,1521,1690,1694,1715,1815,

%U 1875,1936,2028,2178,2312,2366,2401,2420,2535,2541,2601,2662,2704,2890,3025,3042,3125,3267,3380

%N 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.

%C 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.

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

%C 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.

%e A349194(122) = 1*(1+2)*(1+2+2) = 15 and A349278(23) = 3*(3+2) = 15, hence, 15 is not a term.

%e 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.

%e 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.

%Y Cf. A349194, A349278.

%Y Equals A349865 \ A349733.

%K nonn,more,base

%O 1,1

%A _Bernard Schott_, Dec 12 2021

%E a(6)-a(50) from _Michel Marcus_, Dec 12 2021