A358155 First of four consecutive primes p,q,r,s such that (2*p+q)/5, (q+r)/10 and (r+2*s)/5 are prime.

11, 2696717, 3500381, 3989903, 4515113, 8164073, 12451013, 18793013, 23567267, 24057713, 30312409, 36391853, 44569853, 45657881, 53442343, 54721253, 54944761, 56652203, 63993803, 76763081, 90662303, 92889127, 94670143, 105790973, 106339481, 108988223, 117213871, 118802533, 130741007, 145543523

Offset

1,1

Comments

11 is the only term that is in A007530, because if p is in A007530 (so q = p+2, r = p+6 and s = p+8), one of p, q, r, s, 2*p+q, q+r and r+2*s is divisible by 7.

Links

Robert Israel, Table of n, a(n) for n = 1..250

Example

a(3) = 3500381 is a term because 3500381, 3500383, 3500407, 3500429 are four consecutive primes with (2*3500381 + 3500383)/5 = 2100229, (3500383 + 3500407)/10 = 700079, and (3500407 + 2*3500429)/5 = 2100253 all prime.

Maple

Res:= NULL: count:= 0:
q:= 2: r:= 3: s:= 5:
while count < 40 do
  p:= q; q:= r; r:= s; s:= nextprime(s);
  t:= (2*p+q)/5; u:= (q+r)/10; v:= (r+2*s)/5;
  if (t::integer and u::integer and v::integer and isprime(t) and isprime(u) and isprime(v)) then
    count:= count+1; Res:= Res, p;
  fi
od:
Res;

Mathematica

Select[Partition[Prime[Range[8.3*10^6]], 4, 1], PrimeQ[(2*#[[1]] + #[[2]])/5] && PrimeQ[(#[[2]] + #[[3]])/10] && PrimeQ[(#[[3]] + 2*#[[4]])/5] &][[;; , 1]] (* Amiram Eldar, Nov 01 2022 *)

Crossrefs

Cf. A007530, A358149.

Sequence in context: A013858 A230376 A352711 * A083443 A374238 A174089

Adjacent sequences: A358152 A358153 A358154 * A358156 A358157 A358158

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Nov 01 2022

Status

approved