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A181938 Isolated primes = 1 mod 6: sandwiched by primes = 5 mod 6. 2
7, 13, 19, 43, 97, 103, 109, 127, 139, 181, 193, 229, 241, 283, 307, 313, 349, 397, 409, 421, 457, 463, 487, 499, 643, 691, 709, 769, 787, 811, 823, 829, 853, 859, 877, 883, 907, 919, 937, 967, 1021, 1051, 1093, 1153, 1171, 1279, 1303, 1423, 1429, 1447, 1483 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Primes p(m) = 1 mod 6 such that both p(m-1) and p(m+1) are congruent to 5 mod 6.

Corresponding indices m are 4, 6, 8, 14, 25, 27, 29, 31 (A181978).

Note that values of d = p(m+1) - p(m-1) are multiples of 6.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

EXAMPLE

7 = p(4) = 1 mod 6 and both p(3) = 5 and p(5) = 11 are congruent to 5 mod 6,

13 = p(6) = 1 mod 6 and both p(5) = 11 and p(7) = 17 are congruent to 5 mod 6,

43 = p(14) = 1 mod 6 and both p(13) = 41 and p(15) = 47 are congruent to 5 mod 6.

MATHEMATICA

Select[Prime[Range[2, 300]], Mod[#, 6] == 1 && Mod[NextPrime[#, -1], 6] == 5 && Mod[NextPrime[#, 1], 6] == 5 &] (* T. D. Noe, Apr 04 2012 *)

Transpose[Select[Partition[Prime[Range[250]], 3, 1], Mod[#[[1]], 6] == Mod[#[[3]], 6] == 5&&Mod[#[[2]], 6]==1&]][[2]] (* Harvey P. Dale, Sep 17 2012 *)

CROSSREFS

Cf. A002476, A039704, A055625, A181978, A210248.

Sequence in context: A005471 A249381 A040096 * A073648 A298737 A109558

Adjacent sequences:  A181935 A181936 A181937 * A181939 A181940 A181941

KEYWORD

nonn

AUTHOR

Zak Seidov, Apr 03 2012

STATUS

approved

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Last modified April 13 19:42 EDT 2021. Contains 342941 sequences. (Running on oeis4.)