A365309 Primes p such that the six consecutive primes starting with p are congruent to {6, 5, 4, 3, 2, 1} (mod 7).

73471, 307537, 634577, 777671, 1381141, 1886107, 1907527, 2449327, 2505187, 3078431, 3110771, 3299323, 4076477, 4088587, 4666801, 4829257, 4930043, 5069567, 5209301, 5416291, 5513941, 5711551, 6049567, 6053627, 6217091, 7216691, 8057867, 8352301, 8476817, 8635717, 8821231, 8848811, 9073819

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..2000

Example

The six consecutive primes starting with a(3) = 634577 are 634577, 634597, 634603, 634609, 634643, 634649, which are congruent to 6, 5, 4, 3, 2, 1 respectively (mod 7).

Maple

P:= [0$6]: P7:= [0$6]: E:= [seq(i, i=6..1, -1)];
R:= NULL: count:= 0: p:= 0:
while count < 10 do
  p:= nextprime(p);
  P:= [op(P[2..6]), p];;
  P7:= [op(P7[2..6]), p mod 7];
  if P7 = E then count:= count+1; R:= R, P[1]; fi
od:
R;

Mathematica

Prime/@SequencePosition[Mod[Prime[Range[610000]], 7], {6, 5, 4, 3, 2, 1}][[;; , 1]] (* Harvey P. Dale, Sep 20 2023 *)

Crossrefs

Cf. A215599.

Sequence in context: A184769 A242805 A250838 * A105648 A337740 A180300

Adjacent sequences: A365306 A365307 A365308 * A365310 A365311 A365312

Keyword

nonn

Author

Zak Seidov and Robert Israel, Aug 31 2023

Status

approved