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

Author

Harvey P. Dale, Oct 14 2017

Keywords

• nonn
• base
• easy
• fini
• full

Comments

Zero can be a leading digit.

The sequence is the 8-digit analog to A263194.

This sequence contains 5050 terms. - David A. Corneth, Oct 14 2017

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)

Crossrefs

Cf. A037156, A263194.

Programs

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

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

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