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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

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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