A293686 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.
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
Offset: 1
Examples
131299 is a term because 0013 + 1299 = 1312 and 1312 is the string of the middle four digits of 00131299.
Links
- David A. Corneth, Table of n, a(n) for n = 1..5050 (full sequence; first 1045 terms from Vincenzo Librandi)
Programs
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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
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Mathematica
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] -
PARI
is(n) = n < 10^8 && n\10000 + n%10000 == (n \ 100) % 10000 \\ David A. Corneth, Oct 14 2017
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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
Comments