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A052243 Initial prime in set of 4 consecutive primes in arithmetic progression with difference 30. 20
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

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

Index entries for sequences related to primes in arithmetic progressions

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-Fran├žois 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) nextA052243(p, d=[30, 30, 30])={p=[p, 0, 0]; while(p+d!=p=[nextprime(p[1]+1), p[1], p[2]], ); p[3]-d[3]}

p=0; A052243=vector(30, i, p=nextA052243(p+1)) \\ M. F. Hasler, Apr 12 2008

(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} \\ nextA052243(p)=A052243(1, p+1) is over 8 times faster than the code from 2008. - M. F. Hasler, Oct 26 2018

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).

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

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Last modified January 18 16:40 EST 2019. Contains 319271 sequences. (Running on oeis4.)