A241120 -id:A241120 - cp's OEIS frontend

A235705 Primes p such that (p^3 + 6)/5 is prime.

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

K. D. Bajpai, Apr 20 2014

nonn

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

			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.

K. D. Bajpai, Table of n, a(n) for n = 1..2640

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).

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);

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*)

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

A254039 Primes p such that (p^3 + 2)/3, (p^5 + 2)/3 and (p^7 + 2)/3 are prime.

Original entry on oeis.org

524521, 1090891, 1383391, 2633509, 3371059, 4872331, 7304131, 7756669, 8819119, 8877331, 11536471, 12290851, 13362211, 13509649, 14658499, 15359401, 17094151, 17582329, 18191179, 18550891, 19416259, 20465209, 21971629, 22519531, 22619431, 25972561, 27155881, 29281699

Offset: 1

K. D. Bajpai, Jan 23 2015

nonn

All the terms in this sequence are 1 mod 9.

			a(1) = 524521;
(524521^3 + 2)/3 = 48102471044890921;
(524521^5 + 2)/3 = 13234061480615091039311002201;
(524521^7 + 2)/3 = 3640985160809159281478976663465873196681;
all four are prime.

K. D. Bajpai, Table of n, a(n) for n = 1..733

Cf. A241120, A253941, A253976, A253940.

[p: p in PrimesInInterval(3, 10000000) | IsPrime((p^3 + 2) div 3) and IsPrime((p^5 + 2) div 3) and IsPrime((p^7 + 2) div 3)]; // Vincenzo Librandi, Mar 27 2015

Select[Prime[Range[10^7]], PrimeQ[(#^3 + 2)/3] && PrimeQ[(#^5 + 2)/3] && PrimeQ[(#^7 + 2)/3] &]

is(n)=n%9==1 && isprime(n) && isprime((n^3+2)/3) && isprime((n^5+2)/3) && isprime((n^7+2)/3) \\ Charles R Greathouse IV, Jan 23 2015

A256811 Primes p such that (p^2+2)/3 and (p^4+2)/3 are prime.

Original entry on oeis.org

37, 521, 881, 1619, 2053, 2213, 2341, 3527, 3637, 3727, 4157, 5147, 7019, 10009, 10891, 12277, 14741, 15913, 16273, 17747, 18757, 24499, 25307, 25577, 26209, 27073, 31481, 31517, 32833, 35083, 36739, 36791, 39079, 40231, 40949, 41039, 42013, 42461, 42767, 47917

Offset: 1

K. D. Bajpai, Apr 15 2015

			a(1) = 37; (37^2 + 2)/3 = 457; (37^4 + 2)/3 = 624721; all three are prime.

K. D. Bajpai, Table of n, a(n) for n = 1..10000

Cf. A241120, A253941, A253976, A253940.

[p: p in PrimesUpTo(5*10^4) | IsPrime((p^2+2) div 3)  and IsPrime((p^4+2) div 3 )]; // Vincenzo Librandi, Apr 20 2015

Select[Prime[Range[10^4]], PrimeQ[(#^2 + 2)/3] && PrimeQ[(#^4 + 2)/3] &]

forprime(p=1,10^5,if(!((p^2+2)%3)&&!((p^4+2)%3)&&isprime((p^2+2)/3)&&isprime((p^4+2)/3),print1(p,", "))) \\ Derek Orr, Apr 16 2015

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A235705 Primes p such that (p^3 + 6)/5 is prime.

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A254039 Primes p such that (p^3 + 2)/3, (p^5 + 2)/3 and (p^7 + 2)/3 are prime.

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A256811 Primes p such that (p^2+2)/3 and (p^4+2)/3 are prime.

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Author

Keywords

Examples

Links

Crossrefs

Programs

Magma

Mathematica

PARI