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

34061, 190409, 248909, 295601, 305147, 313409, 473027, 479639, 531731, 633497, 682079, 693881, 724331, 777479, 877469, 896201, 1011827, 1088309, 1137341, 1152527, 1179047, 1181777, 1190081, 1210289, 1216619, 1226117, 1272749, 1281587, 1286711, 1305449, 1343801, 1345361, 1357361, 1464179

Offset: 1

Author

N. J. A. Sloane, Jan 17 2012

Keywords

• nonn

Comments

All terms == 5 mod 6. - Zak Seidov, Jan 01 2013

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.

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

Primes p such that A013632(p) = 62. - Robert Israel, Jul 02 2015

Links

• M. F. Hasler, Table of n, a(n) for n = 1..8496 (all terms up to 10^8).
• Index entries for primes, gaps between

Crossrefs

Cf. A013632, A226657.

Programs

Magma

[n: n in [2..2*10^6 ] | (NextPrime(n)-NextPrime(n-1)) eq 62]; // Vincenzo Librandi, Jul 02 2015

Maple

p:= 2:
count:= 0:
while count < 40 do
  q:= nextprime(p);
  if q - p = 62 then
    count:= count+1;
    A[count]:= p;
  fi;
  p:= q;
od:
seq(A[i],i=1..count); # Robert Israel, Jul 02 2015

Mathematica

Select[Prime@ Range@ 120000, NextPrime@ # - # == 62 &] (* Michael De Vlieger, Jul 01 2015 *)
Select[Partition[Prime[Range[120000]],2,1],#[[2]]-#[[1]]==62&][[All,1]] (* Harvey P. Dale, Apr 01 2017 *)

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