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%I #12 Mar 08 2015 18:49:58
%S 1,3,6,17,24,30,50,64,76,86,124,136,171,180,209,240,290,303,359,385,
%T 417,436,521,547,595,643,696,747,823,850,947,982,1022,1102,1171,1234,
%U 1313,1381,1453,1525,1642,1688,1810,1855,1931,2033,2168,2203
%N Positions of squares in the EKG sequence (A064413).
%C Conjecture: the squares appear in increasing order.
%C It appears after inspecting 40000 terms that all the n-th powers (squares, cubes, etc.) appear in increasing order. - _Jacques Tramu_, May 10 2008
%C The conjecture is false; in the EKG sequence, 158^2 is at position 24142, but 157^2 is at position 24146. Note that 157 is prime. If we let p=157, then the two terms on either side of p^2 are p(p+2) and p(p+3), which is unusual because for all primes 3 < p < 157, the three terms are p(p+1), p^2, p(p+2). The next unusual prime is 661. There are no others less than 8164.
%H Zak Seidov and Jacques Tramu, May 10 2008, <a href="/A139476/b139476.txt">Table of n, a(n) for n = 1..143</a>
%e The position of 2^2 = 4 is 3 - the second term in the sequence.
%e The position of 3^2 = 9 is 6 - the third term in the sequence.
%Y Cf. A064413, A064955.
%K nonn
%O 1,2
%A _Zak Seidov_, May 10 2008
%E Edited by _N. J. A. Sloane_, Aug 06 2008
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