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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). 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 3 23:01 EST 2023. Contains 360045 sequences. (Running on oeis4.)