A239543 a(n) is the minimum number greater than a(n-1) such that the concatenation a(n) U a(n-1) U ... U a(1) is a Niven number, starting with a(1)=1.

1, 2, 6, 71, 73, 114, 141, 147, 150, 192, 255, 480, 824, 871, 879, 1014, 1270, 1331, 1359, 1458, 2244, 2547, 2635, 3021, 3447, 3575, 3984, 4035, 4138, 4187, 4554, 6042, 6419, 6431, 6602, 6765, 7074, 7599, 7878, 8163, 9768, 9948, 9975, 10397, 11572, 11961, 12025

Offset

1,2

Links

Paolo P. Lava and Giovanni Resta, Table of n, a(n) for n = 1..5000 (first 100 terms from Paolo P. Lava)

Formula

Starting with a(1)=1, the minimum number a(2) such that a(2) U a(1) is a Niven number is 2. In fact 21 / 3 = 7.

Again the minimum a(3) such that a(3) U a(2) U a(1) is a Niven number is 6. In fact 621 / 9 = 69. Etc.

Maple

with(numtheory);
S:=proc(s) local w; w:=convert(s, base, 10); sum(w[j], j=1..nops(w)); end:
T:=proc(t) local w, x, y; x:=t; y:=0; while x>0 do x:=trunc(x/10); y:=y+1; od; end:
P:=proc(q) local a, b, c, j, n;  a:=1; j:=1; print(1);
for n from 1 to q do b:=T(a); c:=j*10^b+a;
if type(c/S(c), integer) then a:=j*10^b+a; print(j); fi;
j:=j+1; od; print(); end: P(10^6);

Crossrefs

Cf. A005349, A239542.

Sequence in context: A129785 A000896 A103527 * A180982 A195690 A359365

Adjacent sequences: A239540 A239541 A239542 * A239544 A239545 A239546

Keyword

nonn,base

Author

Paolo P. Lava, Mar 21 2014

Status

approved