A116244 Numbers k such that k * (k + 8) is the concatenation of two numbers m and m-7.
94, 461, 532, 714, 818, 994, 3424, 6569, 9994, 90903, 99994, 980198, 999994, 3636357, 6363636, 9999994, 41176464, 58823529, 99999994, 413533834, 426573426, 428571422, 432620005, 567379988, 571428571, 573426567
Offset: 1
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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Maple
F:= proc(d) local R, t,alpha, beta, gamma, delta, B,C,n,m,i0,i,gamma0, delta0; R:= NULL; t:= 10^d+1; for alpha in numtheory:-divisors(t) do beta:= t/alpha; if igcd(alpha,beta) > 1 then next fi; delta0:= 6/beta mod alpha; gamma0:= (beta*delta0-6)/alpha; B:= 2*alpha*gamma0 + 6; C:= gamma0*delta0 - 10^(d-1) - 7; if C < 0 then i0:= 0 else i0:= ceil((-B + sqrt(B^2-4*t*C))/(2*t)) fi; for i from i0 do gamma:= gamma0 + i*beta; delta:= delta0 + i*alpha; m:= gamma*delta; if m -7 >= 10^d then break fi; if m - 7 >= 10^(d-1) then R:= R, alpha*gamma-1 fi; od od; sort(convert({R},list)) end proc: seq(op(F(d)),d=1..10); # Robert Israel, Aug 22 2023 -
Mathematica
a[n_] := Module[{solutions = {}, kvalues, e = 2}, While[Length[solutions] < n, sol = Solve[{a*b == 10^e + 1, 10^(e - 1) <= c*d < 10^e, a*c + 6 == b*d, a > 0, b > 0, c > 0, d > 0}, {a, b, c, d}, Integers]; kvalues = (a*c - 1) /. sol; solutions = Union[solutions, kvalues]; e++]; Take[solutions, n]]; a[26] (* Robert P. P. McKone, Aug 22 2023 *)
Comments