Hello Math-Fun, Start with this: THREE, TEN, THREE, SEVEN, TEN, FIVE, SEVEN, FIVE ... where there are indeed: 3 letters inside the pair of "THREE" 10 letters inside the pair of "TEN" 7 letters inside the pair of "SEVEN" 5 letters inside the pair of "FIVE". This "core" is now the seed of an infinite such sequence: 1) Measure the length (in letters) of the "core" (here 34); 2) write this length before and after the core; 3) repeat ad lib. CORE (34 letters) THIRTY-FOUR -----------------THIRTY-FOUR FIFTY-FOUR ---------------------------------------- FIFTY-FOUR etc. Will you find more such "cores" (where each number-name has exactly one copy)? And a way to enter them into the OEIS? Best, É.