A319746 Quasi-Repfigit numbers (or Quasi-Keith numbers)

12, 18, 32, 35, 43, 59, 142, 187, 241, 265, 610, 778, 1521, 2163, 2625, 3267, 3729, 9242, 15905, 16725, 18852, 56207, 63265, 87538, 94596, 333718, 780890, 839383, 959394, 1114534, 1745662, 2198585, 2424613, 2815415, 5501438, 7371962, 9717796, 21010738, 27800086, 31173396

Offset

1,1

Comments

Numbers n>9 with following property: form a sequence b(i) whose initial terms are the t digits of n, later terms given by rule that b(i) = sum of t previous terms; then n - 1 or n + 1 appears in the sequence.

Links

Table of n, a(n) for n=1..40.

Example

a(1) = 12 because 1 + 2 = 3, 2 + 3 = 5, 3 + 5 = 8, 5 + 8 = 13 = 12 + 1.
a(2) = 18 because 1 + 8 = 9, 8 + 9 = 17 = 18 - 1.

Maple

P:=proc(q) local b, k, n, v; for n from 1 to q do b:=ilog10(n)+1;
if b>1 then v:=[]; for k from 1 to b do
v:=[op(v), trunc(n/10^(b-k)) mod 10]; od; v:=[op(v), add(v[k], k=1..b)];
while v[nops(v)]<n-1 do v:=[op(v), add(v[k], k=nops(v)-b+1..nops(v))]; od;
if v[nops(v)]=n-1 or v[nops(v)]=n+1 then print(n); fi; fi; od; end: P(10^7);

Crossrefs

Cf. A007629, A130010.

Sequence in context: A257768 A007371 A277725 * A079479 A293692 A349027

Adjacent sequences: A319743 A319744 A319745 * A319747 A319748 A319749

Keyword

nonn,base

Author

Paolo P. Lava, Sep 27 2018

Status

approved