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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 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.

LINKS

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

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

Cf. A064413, A064955.

Sequence in context: A036050 A173877 A101525 * A063618 A217084 A024823

Adjacent sequences:  A139473 A139474 A139475 * A139477 A139478 A139479

KEYWORD

nonn

AUTHOR

Zak Seidov, May 10 2008

EXTENSIONS

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

STATUS

approved

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Last modified January 24 13:24 EST 2020. Contains 331193 sequences. (Running on oeis4.)