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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
Each term is congruent to 3 mod 10 (as noted by Zak Seidov in the SeqFan email list). This means the three following consecutive primes are always congruent to 1, 9, and 7 mod 10, respectively (i.e., final digits for these primes are 3, 1, 9, 7, in that order). There cannot be a set of 5 such consecutive primes because a(n) + 4*18 == 5 (mod 10) so is a multiple of 5. - Rick L. Shepherd, Mar 27 2023
LINKS
EXAMPLE
{74453, 74471, 74489, 74507} is the first such set of 4 consecutive primes with common difference 18, so a(1) = 74453.
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-François 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].
Sequence in context: A122065 A079543 A033450 * A234725 A058415 A238521
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Labos Elemer, Jan 31 2000
Definition clarified by Harvey P. Dale, Jun 17 2014
Example reflecting final digits given by Rick L. Shepherd, Mar 27 2023
STATUS
approved

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Last modified June 12 20:44 EDT 2024. Contains 373360 sequences. (Running on oeis4.)