A052243 Initial prime in set of (at least) 4 consecutive primes in arithmetic progression with difference 30.

642427, 1058861, 3431903, 4176587, 4560121, 4721047, 5072269, 5145403, 5669099, 5893141, 6248969, 6285047, 6503179, 6682969, 8545357, 8776121, 8778739, 9490571, 9836227, 9843019, 9843049, 10023787, 11697979, 12057919, 12340313, 12687119, 12794641, 12845849

Offset

1,1

Comments

Primes p such that p, p+30, p+60, p+90 are consecutive primes.

The analogous sequence for a CPAP-5 (at least five consecutive primes in arithmetic progression) with gap 30 does not have its own entry in the OEIS, but for over 500 terms it is identical to A059044. The CPAP-6 analog is A058362. - M. F. Hasler, Jan 02 2020

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000 (terms n = 1..200 from M. F. Hasler)

OEIS wiki, Consecutive primes in arithmetic progression: CPAP with given gap, updated Jan. 2020.

Index entries for sequences related to primes in arithmetic progressions

Formula

A052243 = { A052195(n) | A052195(n+1) = A052195(n) + 30 }. - M. F. Hasler, Jan 02 2020

Example

642427, 642457, 642487, 642517 are consecutive primes, so 642427 is in the sequence.

Maple

p := 2 : q := 3 : r := 5 : s := 7 : for i from 1 do if q-p = 30 and r-q=30 and s-r=30 then printf("%d, \n", p) ; fi ; p := q ; q := r ; r := s ; s := nextprime(r) ; od: # R. J. Mathar, Apr 12 2008

Mathematica

p=2; q=3; r=5; s=7; A052243 = Reap[For[i=1, i<1000000, i++, If[ q-p == 30 && r-q == 30 && s-r == 30 , Print[p]; Sow[p]]; p=q; q=r; r=s; s=NextPrime[r]]][[2, 1]] (* Jean-François Alcover, Jun 28 2012, after R. J. Mathar *)
Transpose[Select[Partition[Prime[Range[1100000]], 4, 1], Union[ Differences[#]] =={30}&]][[1]] (* Harvey P. Dale, Jun 17 2014 *)

Prog

(PARI) A052243(n, p=2, print_all=0, g=30, c, o)={forprime(q=p+1, , if(p+g!=p=q, next, q!=o+2*g, c=2, c++>3, print_all&& print1(o-g", "); n--||break); o=q-g); o-g} \\ optional 2nd arg specifies starting point, allows to define:
next_A052243(p)=A052243(1, p+1) \\ replacing older code from 2008. - M. F. Hasler, Oct 26 2018
(Magma) f:=func<n|NextPrime(n)>; a:=[]; for p in PrimesInInterval(2, 13000000) do if  (f(p)-p eq 30) and (f(f(p))-p eq 60) and (f(f(f(p)))-p eq 90) then Append(~a, p); end if; end for; a; // Marius A. Burtea, Jan 04 2020

Crossrefs

Analogous sequences (start of CPAP-4 with common difference in square brackets): A033451 [6], A033447 [12], A033448 [18], A052242 [24], A052243 [this: 30], A058252 [36], A058323 [42], A067388 [48], A259224 [54], A210683 [60].

Subsequence of A052195 and of A054800 (start of CPAP-4 with any common difference).

See also A059044 (start of CPAP-5), A058362 (CPAP-6).

Sequence in context: A210010 A179576 A089220 * A102810 A159922 A154873

Adjacent sequences: A052240 A052241 A052242 * A052244 A052245 A052246

Keyword

nonn

Author

Labos Elemer, Jan 31 2000

Extensions

More terms from Harvey P. Dale, Nov 19 2000

Edited by N. J. A. Sloane, Apr 28 2008, at the suggestion of R. J. Mathar

Status

approved