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A116136 Numbers k such that k concatenated with k-3 gives the product of two numbers which differ by 4.

%I A116136 #17 Feb 19 2024 20:59:42
%S A116136 9,99,183,328,528,715,999,6099,9999,13224,40495,99999,106755,453288,
%T A116136 999999,2066115,2975208,9999999,22145328,28027683,99999999,110213248,
%U A116136 110667555,147928995,178838403,226123528,275074575,333052608,378698224,445332888,446245635,518348515
%N A116136 Numbers k such that k concatenated with k-3 gives the product of two numbers which differ by 4.
%C A116136 Also numbers k such that k concatenated with itself gives the product of two numbers which differ by 2.
%H A116136 Chai Wah Wu, <a href="/A116136/b116136.txt">Table of n, a(n) for n = 1..10000</a>
%e A116136 8315420899//8315420896 = 9118892968 * 9118892972, where // denotes concatenation.
%o A116136 (Python)
%o A116136 from itertools import count, islice
%o A116136 from sympy import sqrt_mod
%o A116136 def A116136_gen(): # generator of terms
%o A116136     for j in count(0):
%o A116136         b = 10**j
%o A116136         a = b*10+1
%o A116136         for k in sorted(sqrt_mod(1,a,all_roots=True)):
%o A116136             if a*(b+3) <= k**2-1 < a*(a+2):
%o A116136                 yield (k**2-1)//a
%o A116136 A116136_list = list(islice(A116136_gen(),40)) # _Chai Wah Wu_, Feb 19 2024
%Y A116136 Cf. A116129, A115431, A116099, A115426, A116267.
%Y A116136 Cf. also A102567, A116154, A116130, A116286.
%K A116136 nonn,base
%O A116136 1,1
%A A116136 _Giovanni Resta_, Feb 06 2006
%E A116136 Edited by _N. J. A. Sloane_, Apr 15 2007
%E A116136 a(29)-a(32) from _Chai Wah Wu_, Feb 19 2024