

A139476


Positions of squares in the EKG sequence (A064413).


7



1, 3, 6, 17, 24, 30, 50, 64, 76, 86, 124, 136, 171, 180, 209, 240, 290, 303, 359, 385, 417, 436, 521, 547, 595, 643, 696, 747, 823, 850, 947, 982, 1022, 1102, 1171, 1234, 1313, 1381, 1453, 1525, 1642, 1688, 1810, 1855, 1931, 2033, 2168, 2203
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Conjecture: the squares appear in increasing order.
It appears after inspecting 40000 terms that all the nth powers (squares, cubes, etc.) appear in increasing order.  Jacques Tramu, May 10 2008
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.


LINKS



EXAMPLE

The position of 2^2 = 4 is 3  the second term in the sequence.
The position of 3^2 = 9 is 6  the third term in the sequence.


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



