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A293686
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8-digit numbers (padded with leading zeros where necessary) in which the sum of the number consisting of the first four digits and the number consisting of the last four digits equals the number consisting of the middle four digits.
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2
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0, 10099, 10100, 20199, 20200, 30299, 30300, 40399, 40400, 50499, 50500, 60599, 60600, 70699, 70700, 80799, 80800, 90899, 90900, 100999, 101000, 111099, 111100, 121199, 121200, 131299, 131300, 141399, 141400, 151499, 151500, 161599, 161600, 171699, 171700
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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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Zero can be a leading digit.
The sequence is the 8-digit analog to A263194.
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LINKS
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EXAMPLE
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131299 is a term because 0013 + 1299 = 1312 and 1312 is the string of the middle four digits of 00131299.
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MATHEMATICA
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dn8Q[n_]:=Module[{d=PadLeft[IntegerDigits[n], 8, 0]}, FromDigits[ d[[1;; 4]]]+ FromDigits[ d[[5;; 8]]]==FromDigits[d[[3;; 6]]]]; Select[Range[ 0, 10^6], dn8Q]
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PROG
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(Magma) [n: n in [0..2*10^5] | (n div 10000+n) mod 10000 eq (n div 100) mod 10000]; // Vincenzo Librandi, Oct 15 2017
(PARI) is(n) = n < 10^8 && n\10000 + n%10000 == (n \ 100) % 10000 \\ David A. Corneth, Oct 14 2017
(PARI) seq() = {my(t = 0, res = List(), c1, c2); while(t < 10^8, listput(res, t); c2 = (t\10000)%100; if(c2 < 99, t+= 10100, c1 = t\10^6; t = (c1+1)*10^6 + (c1 + 2)*10^4 + 98 - c1)); for(i=2, #res, if(res[i] > 10^6, listsort(res); return(res)); listput(res, res[i]-1))} \\ (this program produces the full sequence) David A. Corneth, Oct 16 2017
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CROSSREFS
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KEYWORD
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nonn,base,easy,fini,full
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AUTHOR
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STATUS
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approved
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