A139476 Positions of squares in the EKG sequence (A064413).

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

Offset: 1

Author

Zak Seidov, May 10 2008

Keywords

• nonn

Comments

Conjecture: the squares appear in increasing order.

It appears after inspecting 40000 terms that all the n-th 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.

Examples

			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.
		

Links

• Zak Seidov and Jacques Tramu, May 10 2008, Table of n, a(n) for n = 1..143

Crossrefs

Cf. A064413, A064955.

Extensions

Edited by N. J. A. Sloane, Aug 06 2008