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A116275 Numbers k such that k*(k+4) gives the concatenation of two numbers m and m-2. 6

%I #16 Feb 21 2024 01:25:33

%S 8872,9009,83352840,99000099,329767122286,670232877711,738226276371,

%T 933006600339,999000000999,3779410975143113,3872816717528065,

%U 4250291784692548,4278630943941865,4372036686326817,4749511753491300,5250488246508697,5627963313673180,5721369056058132

%N Numbers k such that k*(k+4) gives the concatenation of two numbers m and m-2.

%H Chai Wah Wu, <a href="/A116275/b116275.txt">Table of n, a(n) for n = 1..1187</a>

%e 99000099 * 99000103 = 98010199//98010197, where // denotes concatenation.

%o (Python)

%o from itertools import count, islice

%o from sympy import sqrt_mod

%o def A116275_gen(): # generator of terms

%o for j in count(0):

%o b = 10**j

%o a = b*10+1

%o for k in sorted(sqrt_mod(2,a,all_roots=True)):

%o if a*(b+3) <= k**2-2 < a*(a+2):

%o yield k-2

%o A116275_list = list(islice(A116275_gen(),30)) # _Chai Wah Wu_, Feb 19 2024

%Y Cf. A115426, A116267, A116274, A116276, A116288.

%K nonn,base

%O 1,1

%A _Giovanni Resta_, Feb 06 2006

%E a(16)-a(18) from _Chai Wah Wu_, Feb 19 2024

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Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)