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COMMENTS
| Most probably a(5) = 1118176194, because it is a starting point of a string of 5 zeros, but the fact that this is the least such number needs to be confirmed. Note that zeros of A046694(n) have the indices equal to the terms of arithmetic progressions of the type k*p, where primes p belong to A134671 = {1381,5527,8291,12437,22111,29021,30403,34549,37313,...} = Primes of the form 2m*691 - 1. Thus: a(1) = 1381 = 2*691 - 1, a(2) = 16581 = 3*5527 = 3*(8*691 - 1), a(3) = 290217 = 3*96739 = 3*(140*691 - 1), a(4) = 1409635 = 5*281927 = 5*(408*691 - 1), a(5) = 1118176194 = 6*186362699 = 6*(269700*691 - 1). Also, note that all listed terms have the form a(n) = k*p - 1, where prime p is a prime of the form p = 2m*691 - 1 that belong to A134671. a(1) = 2*691 - 1, a(2) = 2*8291 - 1, a(3) = 2*145109 - 1, a(4) = 4*352409 - 1, a(5) = 5*223635239 - 1.
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