A115426 - OEIS

%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