A115428
Numbers k such that the concatenation of k with k+5 gives a square.
Original entry on oeis.org
1, 4, 20, 31, 14564, 38239, 69919, 120395, 426436, 902596, 7478020, 9090220, 6671332084, 8114264059, 8482227259, 9900250996, 2244338786836, 2490577152964, 2509440638591, 2769448208395, 7012067592220
Offset: 1
Cf.
A030465,
A102567,
A115426,
A115437,
A115429,
A115430,
A115431,
A115432,
A115433,
A115434,
A115435,
A115436,
A115439.
A116288
Numbers k such that k*(k+4) gives the concatenation of a number m with itself.
Original entry on oeis.org
7, 97, 451, 546, 689, 854, 997, 4380, 5617, 9997, 72728, 99997, 346531, 653466, 999997, 9090906, 9999997, 94117644, 99999997, 334665331, 336032385, 378253326, 390977440, 439928489, 483516484, 516483513, 560071508
Offset: 1
-
from itertools import count, islice
from sympy import sqrt_mod
def A116288_gen(): # generator of terms
for j in count(0):
b = 10**j
a = b*10+1
for k in sorted(sqrt_mod(4,a,all_roots=True)):
if a*b <= k**2-4 < a*(a-1):
yield k-2
A116288_list = list(islice(A116288_gen(),40)) # Chai Wah Wu, Feb 20 2024
A116296
Numbers k such that k*(k+3) gives the concatenation of two numbers m and m+1.
Original entry on oeis.org
82, 77394228, 89158934, 36623663376237623663376336, 37633762366336633762366236, 62366237633663366237633762, 63376336623762376336623662, 86194223018927804587702129
Offset: 1
89158934 * 89158937 = 79493157//79493158, where // denotes concatenation.
A116298
n times n+7 gives the concatenation of two numbers m and m+1.
Original entry on oeis.org
6, 699, 776, 790, 867, 42337, 57657, 96883, 44121666, 55878328, 85298137, 36680703009575609347721358493, 63319296990424390652278641501, 69346342454876071597336150481, 81501115172242572470460459683
Offset: 1
85298137 * 85298144 = 72757727//72757728, where // denotes
concatenation.
A116317
Numbers k such that k*(k+4) gives the concatenation of two numbers m and m+4.
Original entry on oeis.org
7745, 8019, 33294316, 66705681, 98000199, 340465755423, 476452552743, 523547447254, 659534244574, 866013200679, 998000001999, 3695104677080132, 3755782995538766, 4198081170077529, 4803478892324964, 5196521107675033
Offset: 1
98000199 * 98000203 = 96040393//96040397, where // denotes concatenation.
Showing 1-5 of 5 results.
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