A341217 a(k) is the lesser of the first pair of twin primes that starts a chain of k pairs of twin primes (p(1),p(1)+2), ..., (p(k),p(k)+2) where p(j+1) = 5*p(j)+4.

3, 11, 5, 1720949, 22362444257, 57703877539769

Offset

1,1

Comments

a(5) > 10^8 if it exists.

Links

Table of n, a(n) for n=1..6.

Example

3 and 5 are twin primes, but 5*3+4 = 19 and 21 are not twin primes.
11 and 13 are twin primes, 5*11+4 = 59 and 61 are twin primes, but 5*59+4 = 299 and 301 are not twin primes.
5 and 7 are twin primes, 5*5+4 = 29 and 31 are twin primes, 5*29+4 = 149 and 151 are twin primes, but 5*149+4 = 749 and 751 are not twin primes.
1720949 and 1720951 are twin primes, 5*1720949+4 = 8604749 and 8604751 are twin primes, 5*8604749+4 = 43023749 and 43023751 are twin primes,
5*8604749+4 = 215118749 and 215118751 are twin primes, 5*1075593749+4 = 1075593749 and 1075593751 are not twin primes.

Maple

V:= [3, 0, 0, 0]:
count:= 1:
for p from 5 by 6 while count < 4 do
  if isprime(p) and isprime(p+2) then
    ct:= 1:
    q:= p;
    do
      q:= 5*q+4;
      if not (isprime(q) and isprime(q+2)) then break fi;
      ct:= ct+1;
    od;
    if V[ct] = 0 then V[ct]:= p; count:= count+1; fi;
  fi
od:
V;

Crossrefs

Cf. A001359, A174922.

Sequence in context: A308970 A308971 A120299 * A094900 A196171 A288902

Adjacent sequences: A341214 A341215 A341216 * A341218 A341219 A341220

Keyword

nonn,more

Author

J. M. Bergot and Robert Israel, Feb 06 2021

Extensions

a(5) from Martin Ehrenstein, Feb 07 2021

a(6) from Martin Ehrenstein, Feb 10 2021

Status

approved