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A033448
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Initial prime in set of 4 consecutive primes in arithmetic progression with common difference 18.
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17
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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
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1,1
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COMMENTS
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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
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LINKS
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EXAMPLE
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{74453, 74471, 74489, 74507} is the first such set of 4 consecutive primes with common difference 18, so a(1) = 74453.
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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