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Initial prime in set of 4 consecutive primes with common gap 42.
14

%I #23 Jul 09 2015 05:56:46

%S 23921257,32611897,33215597,35650007,44201617,49945837,51616717,

%T 70350487,70687937,74816107,78789707,86066047,99641917,101568287,

%U 129031187,146922077,149568217,151779517,153921017,156793337,162881627

%N Initial prime in set of 4 consecutive primes with common gap 42.

%C All a(n) == 7 mod 10. - _Robert Israel_, May 13 2015

%H Zak Seidov, <a href="/A058323/b058323.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Pri#primes_AP">Index entries for sequences related to primes in arithmetic progressions</a>

%t d[x_] := Prime[x+1]-Prime[x] {k1=42, k2=42, k3=42} k=0 Do[If[Equal[d[n], k1]&&Equal[d[n+1], k2]&& Equal[d[n+2], k3], k=k+1; Print[{k, n, Prime[n], Prime[n+1], Prime[n+2], Prime[n+3]}]], {n, 1, 10000000}]

%t Transpose[Select[Partition[Prime[Range[9000000]], 4, 1], Union[Differences[#]]=={42}&]][[1]] (* _Vincenzo Librandi_, Jun 21 2015 *)

%Y Analogous sequences (with differences in square brackets): A033451 [6], A033447 [12], A033448 [18], A052242 [24], A052243 [30], A058252 [36].

%K nonn

%O 1,1

%A _Harvey P. Dale_, Dec 12 2000

%E More terms from _Labos Elemer_, Jan 11 2002

%E Definition corrected by _Robert Israel_, May 13 2015

%E Definition edited by _Zak Seidov_, Jun 21 2015

%E Offset changed 0 -> 1 by _Zak Seidov_, Jun 21 2015