OFFSET
1,1
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. 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.
LINKS
Eric Weisstein's World of Mathematics, Ramanujan's Tau Function
EXAMPLE
MAPLE
A134670 := proc(n)
option remember;
if n = 1 then
1381 ;
else
for a from procname(n-1)+1 do
wrks := true;
for k from a to a+n-1 do
if A046694(k) <> 0 then
wrks := false ;
break;
end if;
end do:
if wrks then
return a;
end if;
end do:
end if;
end proc: # R. J. Mathar, Feb 01 2013
CROSSREFS
KEYWORD
hard,nonn,more
AUTHOR
Alexander Adamchuk, Nov 05 2007
EXTENSIONS
a(5) confirmed by Jud McCranie Oct 17 2020
a(6) by Jud McCranie Oct 17 2020
a(7) by Jud McCranie Oct 19 2020
a(8) by Jud McCranie Oct 22 2020
STATUS
approved