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A052243
Initial prime in set of (at least) 4 consecutive primes in arithmetic progression with difference 30.
23
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
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
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