A116200 -id:A116200 - cp's OEIS frontend

A116172 Numbers k such that k concatenated with k+2 gives the product of two numbers which differ by 5.

2, 74, 59264, 510782, 906902, 81790664, 92776472, 10876856041862, 11796926254874, 18332259798794, 18388650720624, 32624670587648, 32699883214248, 43103618706398, 44916698243804, 66132258426302

Offset: 1

Giovanni Resta, Feb 06 2006

Also numbers k such that k concatenated with k+6 gives the product of two numbers which differ by 3.
Also numbers k such that k concatenated with k+8 gives the product of two numbers which differ by 1.
If k+2 and k-4 have the same number of digits, then k is also in A116132 because k//k+2 = 10^d*k + k + 2 = m*(m+5) then implies k//k-4 = 10^d*k + k - 4 = m*(m+5) - 6 = (m-1)*(m+6). - R. J. Mathar, Aug 10 2008

			92776472//92776474 = 96320542 * 96320547, where // denotes concatenation.
92776472//92776480 = 96320544 * 96320545.
92776472//92776478 = 96320543 * 96320546.

Cf. A116158, A116171, A116173, A116179, A116303.

Cf. A116185, A115430, A116205, A116343, A116200, A116330.

Edited by N. J. A. Sloane, Apr 15 2007

A116193 Numbers k such that k concatenated with k+5 gives the product of two numbers which differ by 5.

Original entry on oeis.org

11, 45, 18281, 32769, 56891, 180689, 330539, 959481, 1850201, 3247409, 4940219, 2425563239, 2575561739, 6003563495, 7245212645, 7770160145, 4983798265289, 5049762270381, 5534298528989, 5603798594169, 21894082450101

Offset: 1

Giovanni Resta, Feb 06 2006

Also numbers k such that k concatenated with k+9 gives the product of two numbers which differ by 3. For proof that this is the same sequence compare A116133.

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

			7770160145//7770160136 = 8814851183 * 8814851192, where // denotes concatenation.

Cf. A116205, A116187, A116349.
Cf. A116179, A115430, A116194, A116200, A116324.
Cf. A116099, A116109, A116231.

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

A116147 Numbers k such that k concatenated with k-2 gives the product of two numbers which differ by 9.

Original entry on oeis.org

4962, 237412345332, 262912791034, 468307643502

Offset: 1

Giovanni Resta, Feb 06 2006

Also, numbers k such that k concatenated with k+6 gives the product of two numbers which differ by 7.

			4962//4960 = 7040 * 7049, where // denotes concatenation.

Cf. A116140, A116146, A116153, A116278.

Cf. A116195, A116200, A116202, A116209, A116332.

Edited by N. J. A. Sloane at the suggestion of Eric Desbiaux, Mar 23 2008

A116207 Numbers k such that k concatenated with k+7 gives the product of two numbers which differ by 5.

Original entry on oeis.org

493, 607, 629, 757, 17927, 33247, 93869, 19467217, 31223879, 72757727, 13454739732766891651472740499, 40093333713615672956030023507, 48089152118689474641229584727, 66424317743191484432891678269

Offset: 1

Giovanni Resta, Feb 06 2006

From Robert Israel, Nov 27 2024: (Start)
If 10^d + 1 has a prime factor p such that 53 is not a square mod p, then there are no terms k where k + 7 has d digits.
For example, there are no terms where d == 2 (mod 4), since in that case 10^d + 1 is divisible by 101, and 53 is not a square mod 101. (End)

			72757727//72757734 = 85298138 * 85298143, where // denotes concatenation.

Robert Israel, Table of n, a(n) for n = 1..85 (all terms with up to 113 digits).

Cf. A116167, A116114, A116200, A116173, A116208, A116180, A116338.

f:= proc(d) # terms where k+7 has d digits
    local S,x,R,k;
    S:= map(t -> rhs(op(t)), [msolve(x*(x+5) = 7, 10^d+1)]);
    R:= NULL:
    for x in S do
      k := (x*(x+5)-7)/(10^d+1);
      if ilog10(k+7) = d - 1 then R:= R,k fi
    od:
    op(sort([R]))
end proc:
map(f, [$1..31]); # Robert Israel, Nov 27 2024

A116331 n times n+5 gives the concatenation of two numbers m and m+6.

Original entry on oeis.org

456, 540, 7666, 72722, 356430, 643566, 9090911, 35294119, 64705877, 335664330, 664335666, 684210521, 818181820, 838056675, 846153848, 866028703, 980125140, 3861386140, 6138613856, 6916125390, 9222488468, 41358246491

Offset: 1

Giovanni Resta, Feb 06 2006

Cf. A116200, A116324, A116330, A116332, A116338.

cp's OEIS Frontend

A116172 Numbers k such that k concatenated with k+2 gives the product of two numbers which differ by 5.

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A116193 Numbers k such that k concatenated with k+5 gives the product of two numbers which differ by 5.

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A116147 Numbers k such that k concatenated with k-2 gives the product of two numbers which differ by 9.

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A116207 Numbers k such that k concatenated with k+7 gives the product of two numbers which differ by 5.

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A116331 n times n+5 gives the concatenation of two numbers m and m+6.

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