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 A263194 4-digit numbers (with leading zeros supplied where necessary) in which the sum of the number consisting of the first two digits and the number consisting of the last two digits equals the number consisting of the middle two digits. 1
 0, 109, 110, 219, 220, 329, 330, 439, 440, 549, 550, 659, 660, 769, 770, 879, 880, 989, 990, 1208, 1318, 1428, 1538, 1648, 1758, 1868, 1978, 2307, 2417, 2527, 2637, 2747, 2857, 2967, 3406, 3516, 3626, 3736, 3846, 3956, 4505, 4615, 4725, 4835, 4945, 5604, 5714, 5824, 5934, 6703, 6813, 6923, 7802, 7912, 8901 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 0 can be a leading digit. REFERENCES George Bredehorn, The Giant Book of Puzzles, Main Street, 2013, page 12. LINKS Aresh Pourkavoos, Website with C code to generate sequence FORMULA The sequence contains stretches where, for some n, a(n) - a(n-1) = 110. EXAMPLE Since 19 + 78 = 97, 1978 is a term. MATHEMATICA fQ[n_] := Block[{d = PadLeft[IntegerDigits@ n, 4]}, FromDigits@ d[[1 ;; 2]] + FromDigits@ d[[3 ;; 4]] == FromDigits@ d[[2 ;; 3]]]; Select[Range[0, 10^4 - 1], fQ] (* Michael De Vlieger, Oct 26 2015 *) PROG (C) #include int main(){   int e = 10; // what base we are using: experiment with different values (values above 10 do not work well)   for (int a = 0; a < e; a++){ // I know these nested loops are inelegant, but they're the easiest way     for (int b = 0; b < e; b++){       for (int c = 0; c < e; c++){         for (int d = 0; d < e; d++){           if ((10*a)+b+(10*c)+d == (10*b)+c){ // if the number formed by the first two digits plus the number formed by the last two digits equals the number formed by the middle two digits             if (e <= 10){             printf("%d%d%d%d, ", a, b, c, d); // print the number             }             else{             printf("%d %d %d %d,  ", a, b, c, d); // print the number with extra spaces             }           }         }       }     }   }   printf("\n");   return 0; } (PARI) is(n) = n < 10000 && n%100 + n \ 100 == (n \ 10) % 100 \\ David A. Corneth, Oct 14 2017 (Python) def ok(n): return (n//100) + (n%100) == (n//10)%100 print([m for m in range(10000) if ok(m)]) # Michael S. Branicky, Jan 25 2021 CROSSREFS Cf. A293686. Sequence in context: A130705 A253431 A253438 * A231701 A051046 A196667 Adjacent sequences:  A263191 A263192 A263193 * A263195 A263196 A263197 KEYWORD base,easy,fini,full,nonn AUTHOR Aresh Pourkavoos, Oct 11 2015 STATUS approved

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Last modified May 27 12:49 EDT 2022. Contains 354097 sequences. (Running on oeis4.)