

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
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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]] (* JeanFrançois 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(og", "); nbreak); o=qg); og} \\ 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



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



