A116268 -id:A116268 - cp's OEIS frontend

A116099 Numbers k such that k concatenated with k-9 gives the product of two numbers which differ by 7.

69, 59898667, 79493157, 13412927190959690154913903, 14163000698458955079906403, 38895475965785687555173929, 40165600438484442828161229, 74294440818366638194239027

Offset: 1

Giovanni Resta, Feb 06 2006

Also numbers k such that k concatenated with k-3 gives the product of two numbers which differ by 5.
Also numbers k such that k concatenated with k+1 gives the product of two numbers which differ by 3.
Also numbers k such that k concatenated with k+3 gives the product of two numbers which differ by 1.

			79493157//79493154 = 89158933 * 89158938, where // denotes concatenation.
79493157//79493158 = 89158934 * 89158937.
79493157//79493160 = 89158935 * 89158936.
79493157//79493148 = 89158932 * 89158939.

Cf. A116098, A116193, A116107, A116230, A116130, A116136, A116205, A116107, A116268.

Cf. A115426, A115428, A116171, A116296, A116170, A116177, A116307.

Edited by N. J. A. Sloane, Apr 12 2007

A116267 Numbers k such that k*(k+4) gives the concatenation of two numbers m and m-3.

Original entry on oeis.org

8, 98, 426, 571, 725, 844, 998, 7808, 9998, 36363, 63634, 99998, 326732, 673265, 999998, 4545452, 5454545, 9999998, 47058821, 52941176, 99999998, 331983805, 332667332, 384615384, 422892896, 475524475, 524475522, 577107101, 615384613, 667332665, 668016192, 719964244

Offset: 1

Giovanni Resta, Feb 06 2006

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Cf. A116136, A116260, A116266, A116268, A116275.

from itertools import count, islice
from sympy import sqrt_mod
def A116267_gen(): # generator of terms
    for j in count(0):
        b = 10**j
        a = b*10+1
        for k in sorted(sqrt_mod(1,a,all_roots=True)):
            if a*(b+3) <= k**2-1 < a*(a+2):
                yield k-2
A116267_list = list(islice(A116267_gen(),20)) # Chai Wah Wu, Feb 19 2024

a(29)-a(32) from Chai Wah Wu, Feb 19 2024

A116261 Numbers k such that k*(k+5) gives the concatenation of two numbers m and m-4.

Original entry on oeis.org

7, 97, 766, 857, 909, 997, 3284, 6712, 9997, 45451, 54545, 99997, 990099, 999997, 8181818, 9999997, 70588232, 99999997, 343130553, 362637362, 363636360, 420053630, 421052631, 497975708, 502024288, 578947365, 579946366

Offset: 1

Giovanni Resta, Feb 06 2006

Cf. A028557, A116130, A116255, A116260, A116262, A116268.

A116269 Numbers k such that k*(k+7) gives the concatenation of two numbers m and m-3.

Original entry on oeis.org

87, 3675, 6319, 8785, 48742, 51252, 87616, 3762553, 6237441, 9217099, 3266298273, 3520463763, 6479536231, 6733701721, 8063694647, 8317860137, 4689524709430934473, 5310475290569065521, 7416797436703661746

Offset: 1

Giovanni Resta, Feb 06 2006

Cf. A116205, A116263, A116268, A116270, A116283.

A116276 Numbers k such that k*(k+5) gives the concatenation of two numbers m and m-2.

Original entry on oeis.org

70, 79822843, 69852478553064869297984899963805, 77473062193002372448027740546437, 77747359197583788609974143907617, 84341826458653210947638195982113, 85367942837521291760016984490249

Offset: 1

Giovanni Resta, Feb 06 2006

			79822843 * 79822848 = 63716866//63716864, where // denotes concatenation.

Cf. A028557, A116107, A116268, A116275, A116277, A116281.

cp's OEIS Frontend

A116099 Numbers k such that k concatenated with k-9 gives the product of two numbers which differ by 7.

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A116267 Numbers k such that k*(k+4) gives the concatenation of two numbers m and m-3.

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A116261 Numbers k such that k*(k+5) gives the concatenation of two numbers m and m-4.

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A116269 Numbers k such that k*(k+7) gives the concatenation of two numbers m and m-3.

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A116276 Numbers k such that k*(k+5) gives the concatenation of two numbers m and m-2.

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