cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-8 of 8 results.

A116168 Numbers k such that k concatenated with k+1 gives the product of two numbers which differ by 8.

Original entry on oeis.org

19, 32, 16284704, 35576083, 15764836187996024260119639732979, 19807200907254352332962649366152, 20298517078413563250826300137112, 30190765850423053042937262322867, 30796637697589506772859224996627
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Comments

Also numbers k such that k concatenated with k+8 gives the product of two numbers which differ by 6.

Examples

			35576083//35576084 = 59645686 * 59645694, where // denotes concatenation.
35576083//35576091 = 59645687 * 59645693.

Crossrefs

Cf. A116161, A116167, A116169, A116174, A116299.
Cf. A116208, A115430, A116215, A116345.

Extensions

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

A116174 Numbers k such that k concatenated with k+2 gives the product of two numbers which differ by 8.

Original entry on oeis.org

1143, 4382, 4943, 24941511, 25058558, 94090583, 616729341438, 638432642423, 978717194478, 994009005983, 1636200161363007, 1710661666314798, 1805005185949007, 1906479843038783, 1986790648039982, 3072104679280383
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Comments

Also numbers k such that k concatenated with k+9 gives the product of two numbers which differ by 6.

Examples

			94090583//94090585 = 97000297 * 97000305, where // denotes concatenation.
94090583//94090592 = 97000298 * 97000304.

Crossrefs

Cf. A116168, A116173, A116175, A116181, A116305.
Cf. A116180, A116169, A116352.

Extensions

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

A116215 Numbers k such that k concatenated with k+8 gives the product of two numbers which differ by 7.

Original entry on oeis.org

92, 180, 332, 486, 536, 9720, 13220, 40502, 941486, 2066120, 2975202, 77854680, 123250136, 162423540, 243964010, 256109750, 356387462, 421110162, 542936282, 547361900, 587114192, 591715970, 685172036, 734693886
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Crossrefs

Cf. A116209, A116168, A116216, A116169, A116346.

A116300 n times n+9 gives the concatenation of two numbers m and m+1.

Original entry on oeis.org

26, 66, 3416102887775247376839416334668635, 3756559953325598880263233435801764, 4313503800489302411917772257282208
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Examples

			66 * 75 = 49//50, where // denotes concatenation.

Links

Crossrefs

Cf. A116169, A116293, A116299, A116306.

Programs

  • Maple
    F:= proc(d) local t, g, Cands:
  t:= 10^d+1;
  if NumberTheory:-QuadraticResidue(85,t) <> 1 then return NULL fi;
  Cands:= map(s -> rhs(op(s)), [msolve(x^2 + 9*x - 1, t)]);
  g:= proc(r) local v; v:= r^2 + 9*r - 1; v >= t*(t-11)/10 and v < t*(t-2) end proc;
  op(sort(select(g, Cands)));
end proc:
map
map(F, [$1..82]); # Robert Israel, Aug 25 2023
  • Python
    from itertools import count, islice
from sympy import sqrt_mod_iter
def A116300_gen(): # generator of terms
    for l in count(1):
        m = 10**l+1
        k, r, dlist = m*(m-11)/10, m*(m-2), []
        for a in sqrt_mod_iter(85,m):
            d = ((a if a&1 else a+m)>>1)-4
            if kA116300_list = list(islice(A116300_gen(),14)) # Chai Wah Wu, May 07 2024

A116162 Numbers k such that k concatenated with itself gives the product of two numbers which differ by 9.

Original entry on oeis.org

2, 92, 180, 332, 486, 536, 992, 9720, 9992, 13220, 40502, 99992, 941486, 999992, 2066120, 2975202, 9999992, 77854680, 99999992, 123250136, 162423540, 243964010, 256109750, 356387462, 421110162, 542936282, 547361900
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Crossrefs

Cf. A116153, A116161, A116169, A116293.

A116175 Numbers k such that k concatenated with k+2 gives the product of two numbers which differ by 9.

Original entry on oeis.org

1122070, 1538990, 3692998, 4422608, 1661985831086046580, 3508493742205242178, 5949206094811297768, 11324756194731856386028, 44020205992737767475178, 55147546334394567747178
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Examples

			4422608//4422610 = 6650265 * 6650274, where // denotes
concatenation.

Crossrefs

Cf. A116169, A116174, A116182, A116306.

A116223 Numbers k such that k concatenated with k+9 gives the product of two numbers which differ by 8.

Original entry on oeis.org

136, 399, 600, 744, 8184, 66951, 134199, 401536, 5289264, 12456744, 41868519, 113342199, 115655064, 142598664, 160143051, 206611575, 227626176, 273422475, 297520656, 359785504, 387353899, 435493131, 440015536
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Crossrefs

Cf. A116210, A116169, A116224, A116354.

A116353 Numbers k such that k*(k+7) gives the concatenation of two numbers m and m+9.

Original entry on oeis.org

27, 67, 3416102887775247376839416334668636, 3756559953325598880263233435801765, 4313503800489302411917772257282209
Offset: 1

Views

Author

Giovanni Resta, Feb 06 2006

Keywords

Examples

			67 * 74 = 49//58, where // denotes concatenation.

Crossrefs

Cf. A116169, A116346, A116352, A116354.
Showing 1-8 of 8 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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