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%I #13 Feb 20 2024 20:16:10
%S 7874,8119,69476962,98010199,108746354942,449212110367,544978035127,
%T 870501316279,998001001999,1428394731903223,1499870932756487,
%U 1806498025502498,1830668275445687,1911470478658759,2255786189655202
%N Numbers k such that the concatenation of k with k+2 gives a square.
%C Numbers k such that k concatenated with k+1 gives the product of two numbers which differ by 2.
%C Numbers k such that k concatenated with k-2 gives the product of two numbers which differ by 4.
%C Numbers k such that k concatenated with k-7 gives the product of two numbers which differ by 6.
%H Chai Wah Wu, <a href="/A115426/b115426.txt">Table of n, a(n) for n = 1..1000</a>
%e 8119//8121 = 9011^2, where // denotes concatenation.
%e 98010199//98010200 = 99000100 * 99000102.
%e 98010199//98010197 = 99000099 * 99000103.
%o (Python)
%o from itertools import count, islice
%o from sympy import sqrt_mod
%o def A115426_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-2) <= k**2-2 < a*(a-3):
%o yield (k**2-2)//a
%o A115426_list = list(islice(A115426_gen(),40)) # _Chai Wah Wu_, Feb 20 2024
%Y Cf. A030465, A102567, A115427, A115428, A115429, A115430, A115431, A115432, A115433, A115434, A115435, A115436, A115437.
%Y Cf. A116106, A116110, A116112, A116125, A116242.
%Y Cf. A116136, A116143, A116107, A116275, A116163, A116099, A116177, A116295.
%K base,nonn
%O 1,1
%A _Giovanni Resta_, Jan 24 2006
%E Edited by _N. J. A. Sloane_, Apr 13 2007
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