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A204669 Primes p such that q-p = 62, where q is the next prime after p.

%I A204669 #30 Sep 08 2022 08:46:01
%S A204669 34061,190409,248909,295601,305147,313409,473027,479639,531731,633497,
%T A204669 682079,693881,724331,777479,877469,896201,1011827,1088309,1137341,
%U A204669 1152527,1179047,1181777,1190081,1210289,1216619,1226117,1272749,1281587,1286711,1305449,1343801,1345361,1357361,1464179
%N A204669 Primes p such that q-p = 62, where q is the next prime after p.
%C A204669 All terms == 5 mod 6. - _Zak Seidov_, Jan 01 2013
%C A204669 There are no two consecutive primes in the sequence, while there are such primes p=prime(m) that q=prime(m+2) is also a term.
%C A204669 First such p's are at indices 554, 908, 1902, 2588, 3035, 5320, 6213, 6881, 7853, 8262, which correspond to 10237391, 15442121, 27374771, 36040469, 41216027, 66544301, 76313597, 83565611, 93112589, 97515359 (respectively). Note that a(554) = 10237391 = A226657(31). - _Zak Seidov_, Jul 01 2015
%C A204669 Primes p such that A013632(p) = 62. - _Robert Israel_, Jul 02 2015
%H A204669 M. F. Hasler, <a href="/A204669/b204669.txt">Table of n, a(n) for n = 1..8496</a> (all terms up to 10^8).
%H A204669 <a href="/index/Pri#gaps">Index entries for primes, gaps between</a>
%p A204669 p:= 2:
%p A204669 count:= 0:
%p A204669 while count < 40 do
%p A204669   q:= nextprime(p);
%p A204669   if q - p = 62 then
%p A204669     count:= count+1;
%p A204669     A[count]:= p;
%p A204669   fi;
%p A204669   p:= q;
%p A204669 od:
%p A204669 seq(A[i],i=1..count); # _Robert Israel_, Jul 02 2015
%t A204669 Select[Prime@ Range@ 120000, NextPrime@ # - # == 62 &] (* _Michael De Vlieger_, Jul 01 2015 *)
%t A204669 Select[Partition[Prime[Range[120000]],2,1],#[[2]]-#[[1]]==62&][[All,1]] (* _Harvey P. Dale_, Apr 01 2017 *)
%o A204669 (PARI) g=62;c=o=0;forprime(p=1,default(primelimit),(-o+o=p)==g&write("c:/temp/b204669.txt",c++" "p-g))  \\ _M. F. Hasler_, Jan 18 2012
%o A204669 (Magma) [n: n in [2..2*10^6 ] | (NextPrime(n)-NextPrime(n-1)) eq 62]; // _Vincenzo Librandi_, Jul 02 2015
%Y A204669 Cf.  A013632, A226657.
%K A204669 nonn
%O A204669 1,1
%A A204669 _N. J. A. Sloane_, Jan 17 2012