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A354177
Numbers m such that the four consecutive primes starting at m are congruent to {2, 3, 5, 7} (mod 11).
0
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.
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
KEYWORD
nonn
AUTHOR
Zak Seidov, Sep 09 2022
STATUS
approved