The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A247278 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A247278

Least integer k > 0 such that k*n - prime(k) is a square.
(history; published version)

#38 by N. J. A. Sloane at Thu Apr 23 12:11:58 EDT 2020

STATUS

editing

approved

#37 by N. J. A. Sloane at Thu Apr 23 12:10:49 EDT 2020

NAME

Least integer k > 0 such that k * n - prime(k) is a square.

STATUS

proposed

editing

Discussion

Thu Apr 23

12:11

N. J. A. Sloane: k*n is clearly better here than k * n .  Just as clearly is easier to read than c l e a r l y

#36 by Michel Marcus at Wed Apr 22 04:09:19 EDT 2020

STATUS

editing

proposed

Discussion

Wed Apr 22

04:44

Bernard Schott: It seems that a(n) = 2 if n = 2*(m^2-m+1) for m>2 or n is in A051890 \ {2,6} (?)

Thu Apr 23

03:35

Bernard Schott: even iff (?), but no proof.

#35 by Michel Marcus at Wed Apr 22 04:08:02 EDT 2020

COMMENTS

Note that k * n - prime(k) < 0 if k > e^(n + 1).

STATUS

reviewed

editing

Discussion

Wed Apr 22

04:09

Michel Marcus: I don't think that  "k * n - prime(k)" is more legible that "k*n - prime(k)", on the contrary

#34 by Alonso del Arte at Tue Apr 21 23:18:08 EDT 2020

STATUS

proposed

reviewed

Discussion

Wed Apr 22

00:21

Zhi-Wei Sun: Yes, "a(n) exists for any n>0" contains a typo. This is why I changed n>0 to n>1.

#33 by Alonso del Arte at Tue Apr 21 23:16:36 EDT 2020

STATUS

editing

proposed

Discussion

Tue Apr 21

23:18

Alonso del Arte: Given that the offset is not changed in this edit, I take it the earlier assertion "a(n) exists for any n > 0" was a simple typo. Also, I have skimmed the Ramanujan Journal paper.

#32 by Alonso del Arte at Tue Apr 21 23:15:57 EDT 2020

NAME

Least integer k > 0 such that k * n - prime(k) is a square.

COMMENTS

Note that k * n - prime(k) < 0 if k > e^(n + 1).

#31 by Alonso del Arte at Tue Apr 21 23:12:50 EDT 2020

EXAMPLE

a(5) = 29 since 29 * 5 - prime(29) = 145 - 109 = 6^2.

#30 by Alonso del Arte at Tue Apr 21 23:03:09 EDT 2020

MATHEMATICA

SQ[n_] := IntegerQ[Sqrt[n]]

Do[k = 1; Label[aa]; If[SQ[k * n - Prime[k]], Print[n, " ", k]; Goto[bb]]; k = k + 1; Goto[aa]; Label[bb]; Continue, {n, 2, 60}]

STATUS

proposed

editing

#29 by Zhi-Wei Sun at Tue Apr 21 22:32:04 EDT 2020

STATUS

editing

proposed