A116292 Numbers k such that k * (k + 8) is the concatenation of a number m with itself.
3, 93, 377, 616, 707, 902, 993, 8760, 9993, 45455, 54538, 99993, 693062, 999993, 8181811, 9999993, 88235287, 99999993, 327935223, 330669331, 363636364, 418318516, 428571429, 461538454, 538461539, 571428564, 581681477, 636363629, 669330662, 672064770, 691571587, 756506652, 781954880, 789473685
Offset: 1
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
-
Maple
q:= proc(d,m) local R,t,a,b,x,q; t:= 10^d+1; R:= NULL; for a in numtheory:-divisors(t) do b:= t/a; if igcd(a,b) > 1 then next fi; for x from chrem([0,-m],[a,b]) by t do q:= x*(x+m)/t; if q >= 10^d then break fi; if q >= 10^(d-1) then R:= R, x fi; od od; sort(convert({R},list)); end proc: seq(op(q(d,8)),d=1..10); # Robert Israel, Apr 09 2025 -
Mathematica
ccnQ[n_]:=With[{ccc=With[{c=n(n+8)},TakeDrop[IntegerDigits[c],IntegerLength[c]/2]]},ccc[[1]]==ccc[[2]]]; Select[Range[10^6],ccnQ]//Quiet (* The program generates the first 14 terms of the sequence. *) (* Harvey P. Dale, Jul 05 2025 *)
Extensions
Name edited and more terms from Robert Israel, Apr 09 2025
Comments