

A052239


Smallest prime p in set of 4 consecutive primes in arithmetic progression with common difference 6n.


11



251, 111497, 74453, 1397609, 642427, 5321191, 23921257, 55410683, 400948369, 253444777, 1140813701, 491525857, 998051413, 2060959049, 4480114337, 55140921491, 38415872947, 315392068463, 15162919459, 60600021611, 278300877401, 477836574947, 1486135570643
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OFFSET

1,1


COMMENTS

See also the less restrictive A054701 where the gaps are multiples 6n.  M. F. Hasler, Nov 06 2018


LINKS



EXAMPLE

a(5) = 642427, 642457, 642487, 642517 are the smallest consecutive primes with 3 consecutive gaps of 30, cf. A052243.
Other terms are also initial terms of corresponding sequences:
a(1) = 251 = A033451(1) = A054800(1), start of first CPAP4 with common gap of 6,
a(2) = 111497 = A033447(1), start of first CPAP4 with common gap of 12,
a(3) = 74453 = A033448(1) = A054800(25), first CPAP4 with common gap of 18,
a(4) = 1397609 = A052242(1), start of first CPAP4 with common gap of 24,
a(5) = 642427 = A052243(1) = A052195(16), first CPAP4 with common gap of 30,
a(6) = 5321191 = A058252(1) = A161534(26), first CPAP4 with common gap 36 = 6^2,
a(7) = 23921257 = A058323(1), start of first CPAP4 with common gap of 42,
a(8) = 55410683 = A067388(1), start of first CPAP4 with common gap of 48,
a(9) = 400948369 = A259224(1), start of first CPAP4 with common gap of 54,
a(10) = 253444777 = A210683(1) = A089234(417), CPAP4 with common gap of 60,
a(11) = 1140813701 = A287547(1), start of first CPAP4 with common gap of 66,
a(12) = 491525857 = A287550(1), start of first CPAP4 with common gap of 72,
a(13) = 998051413 = A287171(1), start of first CPAP4 with common gap of 78,
a(14) = 2060959049 = A287593(1), start of first CPAP4 with common gap of 84,
a(15) = 4480114337 = A286817(1) = A204852(444), common distance 90. (End)


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 *)


PROG

(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=qn); on} \\ M. F. Hasler, Nov 06 2018


CROSSREFS

Range is a subset of A054800: start of 4 consecutive primes in arithmetic progression (CPAP4).
Cf. A054701: gaps are possibly distinct multiples of 6n (not CPAP's).


KEYWORD

nice,nonn


AUTHOR



EXTENSIONS

a(7) corrected and more terms added by Graziano Aglietti (mg5055(AT)mclink.it), Aug 22 2010


STATUS

approved



