It may appear that "the least integer not nameable in fewer than nineteen syllables" is 111777. But "the least integer not nameable in fewer than nineteen syllables" is itself a name consisting of only eighteen syllables, and therefore the least integer not nameable in fewer than nineteen syllables can be named using only eighteen syllables (!).
There are alternative expressions, for example wikipedia mentions "the smallest positive integer not definable in fewer than twelve words" and "the smallest positive integer not definable in under sixty letters".
It may appear that "the least integer not nameable in fewer than nineteen syllables" is 111777. But "the least integer not nameable in fewer than nineteen syllables" is itself a name consisting of only eighteen syllables, and therefore the least integer not nameable in fewer than nineteen syllables can be named using only eighteen syllables (!).
There are alternative expressions, for example wikipedia mentions "the smallest positive integer not definable in fewer than twelve words" and "the smallest positive integer not definable in under sixty letters".