A116242 -id:A116242 - cp's OEIS frontend

A115426 Numbers k such that the concatenation of k with k+2 gives a square.

7874, 8119, 69476962, 98010199, 108746354942, 449212110367, 544978035127, 870501316279, 998001001999, 1428394731903223, 1499870932756487, 1806498025502498, 1830668275445687, 1911470478658759, 2255786189655202

Offset: 1

Giovanni Resta, Jan 24 2006

Numbers k such that k concatenated with k+1 gives the product of two numbers which differ by 2.
Numbers k such that k concatenated with k-2 gives the product of two numbers which differ by 4.
Numbers k such that k concatenated with k-7 gives the product of two numbers which differ by 6.

			8119//8121 = 9011^2, where // denotes concatenation.
98010199//98010200 = 99000100 * 99000102.
98010199//98010197 = 99000099 * 99000103.

Chai Wah Wu, Table of n, a(n) for n = 1..1000

Cf. A030465, A102567, A115427, A115428, A115429, A115430, A115431, A115432, A115433, A115434, A115435, A115436, A115437.
Cf. A116106, A116110, A116112, A116125, A116242.
Cf. A116136, A116143, A116107, A116275, A116163, A116099, A116177, A116295.

from itertools import count, islice
from sympy import sqrt_mod
def A115426_gen(): # generator of terms
    for j in count(0):
        b = 10**j
        a = b*10+1
        for k in sorted(sqrt_mod(2,a,all_roots=True)):
            if a*(b-2) <= k**2-2 < a*(a-3):
                yield (k**2-2)//a
A115426_list = list(islice(A115426_gen(),40)) # Chai Wah Wu, Feb 20 2024

Edited by N. J. A. Sloane, Apr 13 2007

A116237 n times n+6 gives the concatenation of two numbers m and m-8.

Original entry on oeis.org

7, 9, 97, 99, 425, 570, 724, 843, 997, 999, 7807, 9997, 9999, 36362, 63633, 99997, 99999, 326731, 673264, 999997, 999999, 4545451, 5454544, 9999997, 9999999, 47058820, 52941175, 99999997, 99999999, 331983804, 332667331, 384615383

Offset: 1

Giovanni Resta, Feb 06 2006

Cf. A116106, A116229, A116236, A116238, A116242.

A116243 n times n+7 gives the concatenation of two numbers m and m-7.

Original entry on oeis.org

38, 56, 32262230, 67737764, 79321054, 3341093417798787499091, 3861488851737861033959, 4747922651210186579785, 5252077348789813420209, 6138511148262138966035, 6658906582201212500903, 7232275368591793618229

Offset: 1

Giovanni Resta, Feb 06 2006

			79321054 * 79321061 = 62918301//62918294, where // denotes
concatenation.

Cf. A116112, A116238, A116242, A116244, A116250.

A116256 Numbers k such that k*(k+6) gives the concatenation of two numbers m and m-5.

Original entry on oeis.org

6, 96, 450, 545, 688, 853, 996, 4379, 5616, 9996, 72727, 99996, 346530, 653465, 999996, 9090905, 9999996, 94117643, 99999996, 334665330, 336032384, 378253325, 390977439, 439928488, 483516483, 516483512, 560071507

Offset: 1

Giovanni Resta, Feb 06 2006

Cf. A116125, A116242, A116255, A116257, A116262.

A116241 n times n+3 gives the concatenation of two numbers m and m-7.

Original entry on oeis.org

73, 7248, 7933, 86896, 95987, 7450774, 8912861, 3546363535354546353, 4635454646463635463, 5364545353536364535, 6453636464645453645, 31993591495513432827263, 39229430087220380122375

Offset: 1

Giovanni Resta, Feb 06 2006

			8912861 * 8912864 = 7943911//7943904, where // denotes
concatenation.

Cf. A116110, A116234, A116242, A116253.

cp's OEIS Frontend

A115426 Numbers k such that the concatenation of k with k+2 gives a square.

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A116237 n times n+6 gives the concatenation of two numbers m and m-8.

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A116243 n times n+7 gives the concatenation of two numbers m and m-7.

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A116256 Numbers k such that k*(k+6) gives the concatenation of two numbers m and m-5.

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A116241 n times n+3 gives the concatenation of two numbers m and m-7.

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