|
%I #30 Sep 08 2022 08:46:01
%S 34061,190409,248909,295601,305147,313409,473027,479639,531731,633497,
%T 682079,693881,724331,777479,877469,896201,1011827,1088309,1137341,
%U 1152527,1179047,1181777,1190081,1210289,1216619,1226117,1272749,1281587,1286711,1305449,1343801,1345361,1357361,1464179
%N Primes p such that q-p = 62, where q is the next prime after p.
%C All terms == 5 mod 6. - _Zak Seidov_, Jan 01 2013
%C 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 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 Primes p such that A013632(p) = 62. - _Robert Israel_, Jul 02 2015
%H 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 <a href="/index/Pri#gaps">Index entries for primes, gaps between</a>
%p p:= 2:
%p count:= 0:
%p while count < 40 do
%p q:= nextprime(p);
%p if q - p = 62 then
%p count:= count+1;
%p A[count]:= p;
%p fi;
%p p:= q;
%p od:
%p seq(A[i],i=1..count); # _Robert Israel_, Jul 02 2015
%t Select[Prime@ Range@ 120000, NextPrime@ # - # == 62 &] (* _Michael De Vlieger_, Jul 01 2015 *)
%t Select[Partition[Prime[Range[120000]],2,1],#[[2]]-#[[1]]==62&][[All,1]] (* _Harvey P. Dale_, Apr 01 2017 *)
%o (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 (Magma) [n: n in [2..2*10^6 ] | (NextPrime(n)-NextPrime(n-1)) eq 62]; // _Vincenzo Librandi_, Jul 02 2015
%Y Cf. A013632, A226657.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Jan 17 2012
|
