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 A233546 Smallest k such that 6^n+k, 6^n+k+g, 6^n+k+2*g are consecutive primes in arithmetic progression. 4
 11, 35, 65, 41, 221, 655, 515, 263, 4265, 893, 4085, 1031, 3161, 145, 821, 2083, 2101, 433, 3743, 2243, 511, 2623, 5653, 271, 2885, 4157, 18023, 9023, 1151, 4787, 737, 2141, 2833, 6181, 3217, 3635, 715, 4501, 5381, 4231, 13265, 823 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS The sequence starts at n=2 as there is no solution for n=1. The primes are probable primes for n>23. LINKS Pierre CAMI, Table of n, a(n) for n = 2..350 Wikipedia, Consecutive primes in arithmetic progression EXAMPLE 6^2+11=47, 6^2+11+6=53, 6^2+11+2*6=59 and 47, 53, 59 are consecutive primes and k=11 is minimal (since although 6^2+5=41, 6^2+5+6=47, 6^2+5+2*6=53 are primes, they are not consecutive primes), so a(2)=11. (Example clarified by Jonathan Sondow, Dec 16 2013.) MATHEMATICA a[n_] := For[k = 1, True, k = k+2, p = 6^n+k; If[PrimeQ[p], q = NextPrime[p]; r = NextPrime[q]; g = q-p; If[g == r-q, Print["n = ", n, " k = ", k, " g = ", g, " ", {p, q, r}]; Return[k]]]]; Table[a[n], {n, 2, 100}] (* Jean-François Alcover, Dec 17 2013 *) PROG (PFGW & SCRIPT) DIM n, 1 DIM i DIM J DIM k DIM pp DIMS t OPENFILEOUT myf, a(n).txt LABEL a SET n, n+1 IF n>350 THEN END SET i, -1 SET j, 0 SET k, 0 LABEL b SET i, i+2 SETS t, %d, %d, %d, %d\,; n; i; j; k SET pp, 6^n+i PRP pp, t IF ISPRP THEN GOTO c GOTO b LABEL c SET j, j+2 SET pp, 6^n+i+j SETS t, %d, %d, %d, %d\,; n; i; j; k PRP pp, t IF ISPRP THEN GOTO d GOTO c LABEL d IF j%6==0 THEN GOTO e SET i, i+j SET j, 0 GOTO c LABEL e SET k, k+2 SETS t, %d, %d, %d, %d\,; n; i; j; k SET pp, 6^n+i+j+k PRP pp, t IF ISPRP && k==j THEN GOTO h IF ISPRP THEN GOTO f GOTO e LABEL f IF k%6==0 THEN GOTO g SET i, i+j+k SET j, 0 SET k, 0 GOTO c LABEL g SET i, i+j SET j, k SET k, 0 GOTO e LABEL h WRITE myf, t GOTO a CROSSREFS Cf. A231576, A231578, A233550, A233742. Sequence in context: A319971 A118554 A348845 * A092069 A103115 A003777 Adjacent sequences: A233543 A233544 A233545 * A233547 A233548 A233549 KEYWORD nonn AUTHOR Pierre CAMI, Dec 12 2013 STATUS approved

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Last modified April 18 10:01 EDT 2024. Contains 371779 sequences. (Running on oeis4.)