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A132231 Primes congruent to 7 (mod 30). 15

%I #46 Sep 08 2022 08:45:31

%S 7,37,67,97,127,157,277,307,337,367,397,457,487,547,577,607,727,757,

%T 787,877,907,937,967,997,1087,1117,1237,1297,1327,1447,1567,1597,1627,

%U 1657,1747,1777,1867,1987,2017,2137,2287,2347,2377,2437,2467,2557,2617,2647

%N Primes congruent to 7 (mod 30).

%C Primes ending in 7 with (SOD-1)/3 integer where SOD is sum of digits. - _Ki Punches_, Feb 07 2009

%C Intersection of A030432 and A002476. - _Ray Chandler_, Apr 07 2009

%C Only from 4927 on, there are more composite numbers than primes in {7+30k}, see A227869. - _M. F. Hasler_, Nov 02 2013

%C Terms are non-twin primes A007510, except for 7. - _Jonathan Sondow_, Oct 27 2017

%H Reinhard Zumkeller, <a href="/A132231/b132231.txt">Table of n, a(n) for n = 1..1000</a>

%H C. K. Caldwell, <a href="http://primes.utm.edu">The Prime Pages</a>

%H Omar E. Pol, <a href="http://www.polprimos.com/imagenes/cribade30columnas.jpg">Prime numbers in a sieve with 30 columns</a>

%H Omar E. Pol, <a href="http://www.polprimos.com">Sobre el patrón de los números primos</a>

%F a(n) = A158573(n)*30 + 7. - _Ray Chandler_, Apr 07 2009

%F a(n) = A211890(4,n-1) for n <= 5. - _Reinhard Zumkeller_, Jul 13 2012

%t Select[30*Range[0,100]+7,PrimeQ] (* _Harvey P. Dale_, Feb 01 2012 *)

%t Select[Prime[Range[1000]],MemberQ[{7},Mod[#,30]]&] (* _Vincenzo Librandi_, Aug 14 2012 *)

%o (Haskell)

%o a132231 n = a132231_list !! (n-1)

%o a132231_list = [x | k <- [0..], let x = 30 * k + 7, a010051' x == 1]

%o -- _Reinhard Zumkeller_, Jul 13 2012

%o (Magma) [p: p in PrimesUpTo(3000) | p mod 30 eq 7 ]; // _Vincenzo Librandi_, Aug 14 2012

%o (PARI) forstep(p=7,1999,30,isprime(p)&&print1(p",")) \\ _M. F. Hasler_, Nov 02 2013

%Y Cf. A007510, A007528, A010051, A068229, A117047, A129807, A039949, A132230-A132236, A214360.

%K nonn,easy

%O 1,1

%A _Omar E. Pol_, Aug 15 2007

%E Extended by _Ray Chandler_, Apr 07 2009

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Last modified March 18 22:09 EDT 2024. Contains 370951 sequences. (Running on oeis4.)