A052239 Smallest prime p in set of 4 consecutive primes in arithmetic progression with common difference 6n.
251, 111497, 74453, 1397609, 642427, 5321191, 23921257, 55410683, 400948369, 253444777, 1140813701, 491525857, 998051413, 2060959049, 4480114337, 55140921491, 38415872947, 315392068463, 15162919459, 60600021611, 278300877401, 477836574947, 1486135570643
Offset: 1
Examples
a(5) = 642427, 642457, 642487, 642517 are the smallest consecutive primes with 3 consecutive gaps of 30, cf. A052243. From _M. F. Hasler_, Nov 06 2018: (Start) Other terms are also initial terms of corresponding sequences: a(1) = 251 = A033451(1) = A054800(1), start of first CPAP-4 with common gap of 6, a(2) = 111497 = A033447(1), start of first CPAP-4 with common gap of 12, a(3) = 74453 = A033448(1) = A054800(25), first CPAP-4 with common gap of 18, a(4) = 1397609 = A052242(1), start of first CPAP-4 with common gap of 24, a(5) = 642427 = A052243(1) = A052195(16), first CPAP-4 with common gap of 30, a(6) = 5321191 = A058252(1) = A161534(26), first CPAP-4 with common gap 36 = 6^2, a(7) = 23921257 = A058323(1), start of first CPAP-4 with common gap of 42, a(8) = 55410683 = A067388(1), start of first CPAP-4 with common gap of 48, a(9) = 400948369 = A259224(1), start of first CPAP-4 with common gap of 54, a(10) = 253444777 = A210683(1) = A089234(417), CPAP-4 with common gap of 60, a(11) = 1140813701 = A287547(1), start of first CPAP-4 with common gap of 66, a(12) = 491525857 = A287550(1), start of first CPAP-4 with common gap of 72, a(13) = 998051413 = A287171(1), start of first CPAP-4 with common gap of 78, a(14) = 2060959049 = A287593(1), start of first CPAP-4 with common gap of 84, a(15) = 4480114337 = A286817(1) = A204852(444), common distance 90. (End)
Links
Crossrefs
Programs
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Mathematica
Transpose[Flatten[Table[Select[Partition[Prime[Range[2000000]],4,1], Union[ Differences[ #]] =={6n}&,1],{n,7}],1]][[1]] (* Harvey P. Dale, Aug 12 2012 *) -
PARI
a(n, p=[2, 0, 0], d=6*[n, n, n])={while(p+d!=p=[nextprime(p[1]+1), p[1], p[2]], ); p[3]-d[3]} \\ after M. F. Hasler in A052243; Graziano Aglietti (mg5055(AT)mclink.it), Aug 22 2010, Corrected by M. F. Hasler, Nov 06 2018 -
PARI
A052239(n, p=2, c, o)={n*=6; forprime(q=p+1, , if(p+n!=p=q, next, q!=o+2*n, c=2, c++>3, break); o=q-n); o-n} \\ M. F. Hasler, Nov 06 2018
Extensions
More terms from Labos Elemer, Jan 04 2002
a(7) corrected and more terms added by Graziano Aglietti (mg5055(AT)mclink.it), Aug 22 2010
a(15)-a(20) from Donovan Johnson, Oct 05 2010
a(21)-a(23) from Donovan Johnson, May 23 2011
Comments