The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A067076 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A067076

Numbers k such that 2*k + 3 is a prime.
(history; published version)

#92 by N. J. A. Sloane at Wed Feb 14 19:48:30 EST 2024

STATUS

proposed

approved

#91 by M. F. Hasler at Wed Feb 14 14:15:48 EST 2024

STATUS

editing

proposed

#90 by M. F. Hasler at Wed Feb 14 14:14:30 EST 2024

FORMULA

a(n) = A006254(n) - 2 = A086801(n+1)/2. [Corrected by M. F. Hasler, Feb 14 2024]

PROG

(PARI) { n=0; for (m=0, 10^10, if (isprime(2*m + 3), write("b067076.txt", n++, " ", m); if (n==1000, return)) ) } \\ Harry J. Smith, May 05 2010

(PARI) [k | k<-[0..99], isprime(2*k+3)] \\ for illustration

(PARI) A067076(n) = (prime(n+1)-3)/2 \\ M. F. Hasler, Feb 14 2024

#89 by M. F. Hasler at Wed Feb 14 14:04:25 EST 2024

FORMULA

a(n) = A006254(n+1) - 2 = A086801(n)/2. [Corrected by _M. F. Hasler_, Feb 14 2024]

EXTENSIONS

Offset changed from 0 to 1 in 2008: some formulas here and elsewhere may need to be corrected.

STATUS

approved

editing

Discussion

Wed Feb 14

14:08

M. F. Hasler: Cf. https://oeis.org/history?seq=A067076&start=80. It already had the first formula as it was up to today, and it wasn't adjusted when the offset was changed. OTOH, A086801 had a(0)=0 before offset was changed to 1 *and* a(1)= -1 was pre-fixed in 2006 (leading to a shift of indices by 2) !

14:10

M. F. Hasler: this is super confusing !

#88 by Joerg Arndt at Sun Feb 04 01:14:18 EST 2024

STATUS

editing

approved

#87 by Paolo P. Lava at Sat Feb 03 08:00:03 EST 2024

COMMENTS

Solutions of the equation (2*n+3)' = 1, where n' is the arithmetic derivative of n. - Paolo P. Lava, Nov 15 2012

STATUS

approved

editing

#86 by Charles R Greathouse IV at Thu Sep 08 08:45:05 EDT 2022

PROG

(MAGMAMagma)[n: n in [0..200]| IsPrime(2*n+3)]; // Vincenzo Librandi, Feb 23 2012

Discussion

Thu Sep 08

08:45

OEIS Server: https://oeis.org/edit/global/2944

#85 by Sean A. Irvine at Tue May 21 17:50:45 EDT 2019

STATUS

proposed

approved

#84 by G. C. Greubel at Tue May 21 17:44:50 EDT 2019

STATUS

editing

proposed

#83 by G. C. Greubel at Tue May 21 17:44:16 EDT 2019

MATHEMATICA

lst={}; Do[If[PrimeQ(Prime[2*n+3], AppendToRange[lst, n100]+1], {n, 10^-3}]; lst )/2 (* Vladimir Joseph Stephan Orlovsky, Sep 08 2008 , modified by _G. C. Greubel_, May 21 2019 *)

PROG

(Sage) [n for n in (0..200) if is_prime(2*n+3) ] # G. C. Greubel, May 21 2019

(GAP) Filtered([0..200], k-> IsPrime(2*k+3) ) # G. C. Greubel, May 21 2019

STATUS

approved

editing