Search: a116168 -id:a116168
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A115430
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Numbers k such that the concatenation of k with k+9 gives a square.
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+10
18
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216, 287, 515, 675, 1175, 4320, 82640, 960795, 1322312, 4049591, 16955015, 34602080, 171010235, 181964891, 183673467, 187160072, 321920055, 326530616, 328818032, 343942560, 470954312, 526023432, 528925616, 534830855
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OFFSET
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1,1
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COMMENTS
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Also numbers k such that k concatenated with k+8 gives the product of two numbers which differ by 2.
Also numbers k such that k concatenated with k+5 gives the product of two numbers which differ by 4.
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LINKS
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EXAMPLE
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82640_82649 = 90907^2.
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CROSSREFS
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Cf. A030465, A102567, A115426, A115437, A115428, A115429, A115431, A115432, A115433, A115434, A115435, A115436, A115441.
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A116169
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Numbers k such that k concatenated with k+1 gives the product of two numbers which differ by 9.
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+10
8
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OFFSET
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1,1
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COMMENTS
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Also numbers k such that k concatenated with k+9 gives the product of two numbers which differ by 7.
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LINKS
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EXAMPLE
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49//50 = 66 * 75, where // denotes concatenation.
49//58 = 67 * 74.
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A116174
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Numbers k such that k concatenated with k+2 gives the product of two numbers which differ by 8.
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+10
8
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1143, 4382, 4943, 24941511, 25058558, 94090583, 616729341438, 638432642423, 978717194478, 994009005983, 1636200161363007, 1710661666314798, 1805005185949007, 1906479843038783, 1986790648039982, 3072104679280383
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OFFSET
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1,1
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COMMENTS
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Also numbers k such that k concatenated with k+9 gives the product of two numbers which differ by 6.
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LINKS
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EXAMPLE
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94090583//94090585 = 97000297 * 97000305, where // denotes concatenation.
94090583//94090592 = 97000298 * 97000304.
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A116167
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Numbers k such that k concatenated with k+1 gives the product of two numbers which differ by 7.
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+10
6
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7, 493, 607, 629, 757, 17927, 33247, 93869, 19467217, 31223879, 72757727, 13454739732766891651472740499, 40093333713615672956030023507, 48089152118689474641229584727, 66424317743191484432891678269
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OFFSET
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1,1
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LINKS
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EXAMPLE
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72757727//72757728 = 85298137 * 85298144, where // denotes concatenation.
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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A116345
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Numbers k such that k*(k+6) gives the concatenation of two numbers m and m+8.
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+10
6
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41, 54, 40354308, 59645687, 39704957106129738595969799927611, 44505281604832422780051712184760, 45053875613995255103944518907120, 54946124386004744896055481092875, 55494718395167577219948287815235, 60295042893870261404030200072384, 68683652917306421895276391964227
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listen;
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OFFSET
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1,1
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LINKS
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EXAMPLE
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59645687 * 59645693 = 35576083//35576091, where // denotes concatenation.
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MAPLE
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f:= proc(d) local R;
R:= map(rhs@op, {msolve(x^2=17, 10^d+1)});
R:= map(t -> (t-3) mod (10^d+1), R);
op(select(proc(t) local m; m:= (t*(t+6)-8)/(10^d+1)+8; m >= 10^(d-1) and m < 10^d end proc, R));
end proc;
sort(convert({seq(f(i), i=1..50)}, list)); # Robert Israel, Jan 17 2017
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A116161
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Numbers k such that k concatenated with itself gives the product of two numbers which differ by 8.
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+10
5
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3, 93, 145, 384, 505, 820, 993, 7680, 9993, 20665, 29748, 99993, 480340, 999993, 6694209, 9999993, 77854665, 99999993, 107541513, 109342209, 132231408, 174990384, 183673473, 213017748, 289940833, 326530608, 338353345
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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LINKS
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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A116208
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Numbers k such that k concatenated with k+7 gives the product of two numbers which differ by 6.
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+10
5
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145, 384, 505, 820, 7680, 20665, 29748, 480340, 6694209, 77854665, 107541513, 109342209, 132231408, 174990384, 183673473, 213017748, 289940833, 326530608, 338353345, 404958673, 448003540, 451671060, 478271265
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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LINKS
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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A116215
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Numbers k such that k concatenated with k+8 gives the product of two numbers which differ by 7.
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+10
5
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92, 180, 332, 486, 536, 9720, 13220, 40502, 941486, 2066120, 2975202, 77854680, 123250136, 162423540, 243964010, 256109750, 356387462, 421110162, 542936282, 547361900, 587114192, 591715970, 685172036, 734693886
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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LINKS
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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A116299
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n times n+8 gives the concatenation of two numbers m and m+1.
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+10
5
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40, 53, 40354307, 59645686, 39704957106129738595969799927610, 44505281604832422780051712184759, 45053875613995255103944518907119, 54946124386004744896055481092874, 55494718395167577219948287815234
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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LINKS
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EXAMPLE
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59645686 * 59645694 = 35576083//35576084, where // denotes
concatenation.
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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