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A033448 Initial prime in set of 4 consecutive primes in arithmetic progression with common difference 18. 17
74453, 76543, 132893, 182243, 202823, 297403, 358793, 485923, 655453, 735883, 759113, 780613, 797833, 849143, 1260383, 1306033, 1442173, 1531093, 1534153, 1586953, 1691033, 1717063, 1877243, 1945763, 1973633, 2035513, 2067083, 2216803, 2266993, 2542513, 2556803, 2565203, 2805773 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Up to n = 10^4, the smallest difference a(n+1) - a(n) is 60 and occurs at n = 8571. - M. F. Hasler, Oct 26 2018

LINKS

M. F. Hasler, Table of n, a(n) for n = 1..10000

Index entries for sequences related to primes in arithmetic progressions

MATHEMATICA

A033448 = Reap[For[p = 2, p < 2100000, p = NextPrime[p], p2 = NextPrime[p]; If[p2 - p == 18, p3 = NextPrime[p2]; If[p3 - p2 == 18, p4 = NextPrime[p3]; If[p4 - p3 == 18, Sow[p]]]]]][[2, 1]] (* Jean-Fran├žois Alcover, Jun 28 2012 *)

Transpose[Select[Partition[Prime[Range[160000]], 4, 1], Union[ Differences[ #]] == {18}&]][[1]] (* Harvey P. Dale, Jun 17 2014 *)

PROG

(PARI) A033448(n, show_all=1, g=18, p=2, o, c)={forprime(q=p+1, , if(p+g!=p=q, next, q!=o+2*g, c=3, c++>4, print1(o-g", "); n--||break); o=q-g); o-g} \\ Can be used as nxt(p)=A033448(1, , , p+1), e.g.: {p=0; vector(20, i, p=nxt(p))} or {p=0; for(i=1, 1e4, write("b.txt", i" "nxt(p)))}. - M. F. Hasler, Oct 26 2018

CROSSREFS

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

Cf. A033450, A052189.

Sequence in context: A122065 A079543 A033450 * A234725 A058415 A238521

Adjacent sequences:  A033445 A033446 A033447 * A033449 A033450 A033451

KEYWORD

nonn

AUTHOR

Jeff Burch

EXTENSIONS

More terms from Labos Elemer, Jan 31 2000

Definition clarified by Harvey P. Dale, Jun 17 2014

STATUS

approved

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Last modified April 3 14:34 EDT 2020. Contains 333197 sequences. (Running on oeis4.)