A354177 Numbers m such that the four consecutive primes starting at m are congruent to {2, 3, 5, 7} (mod 11).

2, 82799, 406661, 447779, 490019, 596279, 617971, 654931, 790781, 1286969, 1532291, 1543357, 1775831, 1916939, 1932911, 2220539, 2240977, 2298749, 2307989, 2376629, 2435039, 2458139, 2513579, 2731049, 2775599, 3093851, 3141899, 3213839, 3294337, 3331319, 3351251, 3366497, 3645193, 3689149, 3733259, 3781153, 3981331

Offset

1,1

Comments

All first differences except for 82799 - 2 = 82797 are multiples of 22.

Links

Table of n, a(n) for n=1..37.

Example

The four consecutive primes {82799, 82811, 82813, 82837} are congruent to {2, 3, 5, 7} (mod 11).

Maple

R:= 2: count:= 1:
for p from 13 by 22 while count < 37 do
  if not isprime(p) then next fi;
  q:= nextprime(p); if q mod 11 <> 3 then next fi;
  q:= nextprime(q); if q mod 11 <> 5 then next fi;
  q:= nextprime(q); if q mod 11 = 7 then
     count:= count+1; R:= R, p fi
od:
R; # Robert Israel, Sep 14 2022

Mathematica

s = {2}; p1=7; Do[p1 = NextPrime[p1]; p2 = NextPrime[p1]; p3 = NextPrime[p2]; p4 = NextPrime[p3]; If[{2, 3, 5, 7} == Mod[{p1, p2, p3, p4}, 11], AppendTo[s, p1]], {10^6}]; s

Crossrefs

Subsequence of A167134.

Sequence in context: A321246 A371645 A060069 * A231612 A296104 A170995

Adjacent sequences: A354174 A354175 A354176 * A354178 A354179 A354180

Keyword

nonn

Author

Zak Seidov, Sep 09 2022

Status

approved