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A134670 First position k such that A046694(k) = A046694(k+1) =.. 0 are n consecutive zeros starting with A046694(k), where A046694 = Ramanujan tau numbers mod 691. 3
1381, 16581, 290217, 1409635, 1118176194, 107792931954, 673751534392, 2587409974788 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..8.

Eric Weisstein's World of Mathematics, Ramanujan's Tau Function

EXAMPLE

a(1) = 1381 because A046694(1381) = 0 is the first zero in A046694(n).

a(2) = 16581 because A046694(16581) = A046694(16582) = 0 are the first two consecutive zeros in A046694(n).

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

Cf. A046694, A121733, A121734, A121742, A121743.

Sequence in context: A241483 A134671 A161192 * A250367 A092128 A156410

Adjacent sequences:  A134667 A134668 A134669 * A134671 A134672 A134673

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

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Last modified January 19 08:18 EST 2022. Contains 350464 sequences. (Running on oeis4.)