A340574 a(1) = 112. a(n) is the smallest number k with the sum of the even digits equal to the sum of the odd digits (A036301), which is not an earlier term, for which k*a(n - 1) has the sum of the even digits equal to the sum of the odd digits (A036301).

112, 583, 1120, 781, 1452, 615, 1627, 1694, 1506, 1403, 1078, 1043, 538, 121, 4983, 1087, 1708, 1304, 314, 385, 341, 134, 187, 1340, 718, 2123, 358, 1021, 1102, 211, 835, 2110, 1322, 3265, 2558, 561, 1034, 871, 2167, 3085, 1232, 1245, 413, 2716, 1201, 1012, 336

Offset: 1

Author

Marius A. Burtea, Jan 12 2021

Keywords

• nonn
• base

Comments

Sequence only with terms in A036301 for which a(n)*a(n+1) is a term in A036301.

a(1) = 112 = A036301(2) is the first nonzero term of A036301.

The sequence is infinite.

Examples

			a(1) = 112, a(2) = 583 = A036301(22) and a(1)*a(2) = 112*583 = 65296 is a term in A036301 because 6 + 2 + 6 = 14 = 5 + 9.
a(2) = 583, a(3) = 1120 = A036301(41) and a(2)*a(3) = 583*1120 = 652960 is a term in A036301 because 6 + 2 + 6 + 0 = 14 = 5 + 9.
		

Crossrefs

Cf. A036301, A340470.

Programs

Magma

f:=func; a:=[112]; for n in [2..50] do k:=1; while k in a or not f(k) or not f(k*a[n-1]) do k:=k+1; end while; Append(~a,k); end for; a;

PARI

isokd(n) = my(d=digits(n)); sum(k=1, #d, d[k]*(d[k] % 2)) == sum(k=1, #d, d[k]*(1-d[k]%2)); \\ A036301
nextk(va, n) = {my(ok = 0, k = 1); while (! (isokd(k) && isokd(k*va[n-1]) && !#select(x->(x==k), va)), k++); k;}
lista(nn) = {my(va = vector(nn)); va[1] = 112; for (n=2, nn, my(k = nextk(va, n)); va[n] = k;); va;} \\ Michel Marcus, Jan 14 2021