The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A235705 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A235705

Primes p such that (p^3 + 6)/5 is prime.
(history; published version)

#12 by N. J. A. Sloane at Wed Apr 23 16:05:35 EDT 2014

STATUS

reviewed

approved

#11 by Colin Barker at Mon Apr 21 03:45:20 EDT 2014

STATUS

proposed

reviewed

#10 by Colin Barker at Mon Apr 21 03:44:32 EDT 2014

STATUS

editing

proposed

#9 by Colin Barker at Mon Apr 21 03:44:24 EDT 2014

PROG

(PARI) s=[]; forprime(p=2, 20000, if((p^3+6)%5==0 && isprime((p^3+6)/5), s=concat(s, p))); s \\ Colin Barker, Apr 21 2014

STATUS

proposed

editing

#8 by K. D. Bajpai at Sun Apr 20 13:54:52 EDT 2014

STATUS

editing

proposed

#7 by K. D. Bajpai at Sun Apr 20 13:53:57 EDT 2014

LINKS

K. D. Bajpai, <a href="/A235705/b235705.txt">Table of n, a(n) for n = 1..2640</a>

#6 by K. D. Bajpai at Sun Apr 20 13:52:24 EDT 2014

NAME

allocated for K. D. Bajpai

Primes p such that (p^3 + 6)/5 is prime.

DATA

19, 59, 269, 349, 409, 419, 479, 769, 929, 1109, 1319, 1399, 1979, 2609, 3659, 4079, 4919, 5309, 5449, 5879, 6079, 6299, 6949, 7069, 7129, 7229, 7699, 7829, 8069, 8329, 8599, 9679, 10729, 11969, 12809, 13109, 13229, 13859, 14159, 14419, 14629, 14929, 15259

OFFSET

1,1

COMMENTS

All the terms in the sequence are congruent to 1 or 3 mod 4.

EXAMPLE

a(1) = 19 is prime: (19^3 + 6)/ 5 = 1373 which is also prime.

a(2) = 59 is prime: (59^3 + 6)/ 5 = 41077 which is also prime.

MAPLE

KD:= proc() local a, b; a:=ithprime(n); b:=(a^3+6)/5; if b=floor(b) and isprime(b) then RETURN (a); fi; end: seq(KD(), n=1..5000);

MATHEMATICA

Select[Prime[Range[5000]], PrimeQ[(#^3 + 6)/5] &]

n = 0; Do[If[PrimeQ[(Prime[k]^3 + 6)/5], n = n + 1; Print[n, " ", Prime[k]]], {k, 1, 200000}] (*b-file*)

CROSSREFS

Cf. A109953 (primes p: (p^2+1)/3 is prime).

Cf. A118915 (primes p: (p^2+5)/6 is prime).

Cf. A118918 (primes p: (p^2+11)/12 is prime).

Cf. A241101 (primes p: (p^3-4)/3 is prime).

Cf. A241120 (primes p: (p^3+2)/3 is prime).

KEYWORD

allocated

nonn,new

AUTHOR

K. D. Bajpai, Apr 20 2014

STATUS

approved

editing

#5 by K. D. Bajpai at Sun Apr 20 13:52:24 EDT 2014

NAME

allocated for K. D. Bajpai

KEYWORD

recycled

allocated

#4 by R. J. Mathar at Fri Apr 18 19:10:57 EDT 2014

STATUS

editing

approved

#3 by R. J. Mathar at Fri Apr 18 19:10:54 EDT 2014

NAME

allocated for Farideh Firoozbakht

KEYWORD

allocated

recycled

STATUS

approved

editing