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

1,1

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.

Links

Table of n, a(n) for n=1..47.

Example

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.

Prog

(Magma) f:=func<n|&+[(-1)^c*c:c in Intseq(n)] eq 0>; 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

Crossrefs

Cf. A036301, A340470.

Sequence in context: A234674 A217992 A221798 * A189544 A154063 A205250

Adjacent sequences: A340571 A340572 A340573 * A340575 A340576 A340577

Keyword

nonn,base

Author

Marius A. Burtea, Jan 12 2021

Status

approved