The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A335739 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A335739

Numbers k such that the area of an equilateral triangle of side k falls in between twin primes.
(history; published version)

#100 by Joerg Arndt at Wed Oct 06 02:40:18 EDT 2021

STATUS

proposed

approved

#99 by Michel Marcus at Wed Oct 06 02:31:43 EDT 2021

STATUS

editing

proposed

#98 by Michel Marcus at Wed Oct 06 02:31:38 EDT 2021

EXAMPLE

An equilateral triangle of side 17 has an area A = (sqrt(3)/4) * 17^2 = 125.14 which is between 125 and 127. These are not twin primes; so 17 is not a term.

STATUS

approved

editing

#97 by N. J. A. Sloane at Mon Dec 28 15:36:41 EST 2020

STATUS

proposed

approved

#96 by Michel Marcus at Mon Dec 28 10:58:44 EST 2020

STATUS

editing

proposed

Discussion

Mon Dec 28

11:30

David A. Corneth: Philip, yes but Area increases as sides increase and vice versa. So you'd just have to check extremes. Like sides that come with area 3 and 5 respectively and then see if there's an integer between them.

#95 by Michel Marcus at Mon Dec 28 10:58:34 EST 2020

CROSSREFS

Cf. A001359, A006512.

STATUS

proposed

editing

Discussion

Mon Dec 28

10:58

Michel Marcus: missing period

#94 by Philip Mizzi at Mon Dec 28 06:44:44 EST 2020

STATUS

editing

proposed

#93 by Philip Mizzi at Mon Dec 28 06:30:28 EST 2020

DATA

3, 4, 25, 98, 119, 123, 136, 267, 299, 318, 344, 423, 429, 443, 444, 522, 552, 571, 577, 588, 589, 639, 677, 739, 771, 817, 933, 993, 1115, 1212, 1393, 1503, 1558, 1580, 1629, 1756, 1799, 1852, 1871, 1884, 1991, 2027, 2063, 2197, 2345, 2380, 2583, 2585, 2702, 2821, 2887, 2888, 2924, 2957, 3092, 3198, 3466, 3527

Discussion

Mon Dec 28

06:32

David A. Corneth: To ease search one maybe wants to take potential areas between twin primes and compute corresponding side lenghts.

06:44

Philip Mizzi: @David: Happy to learn somthing new but to my mind, wouldn't that be a longer search? I mean there are obviously infinite possible areas between any pair of twin primes and no clear indicator which area might lead to a side length that is an integer.

#92 by Michel Marcus at Mon Dec 28 06:26:15 EST 2020

PROG

(PARI) isok(k) = my(A = floor(k^2*sqrt(3)/4)); if (! (A%2), A--); isprime(A) && isprime(A+2); \\ Michel Marcus, Dec 28 2020

STATUS

proposed

editing

Discussion

Mon Dec 28

06:27

Michel Marcus: I agree with terms; but data section is too big again !

06:29

Philip Mizzi: @Michel: Apologies. I thought I had corrected this. it obviously grew as I added more terms.

#91 by Philip Mizzi at Mon Dec 28 06:11:13 EST 2020

STATUS

editing

proposed