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A112794 Primes such that the sum of the predecessor and successor primes is divisible by 5. 15
5, 11, 19, 41, 71, 73, 89, 97, 101, 109, 137, 149, 181, 229, 241, 281, 293, 311, 349, 359, 389, 397, 409, 419, 421, 433, 449, 457, 461, 487, 541, 557, 587, 631, 701, 709, 743, 751, 787, 811, 859, 881, 887, 919, 937, 991, 997, 1009, 1021, 1033, 1049, 1051, 1063 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
FORMULA
a(n) = prime(i) is in this sequence iff prime(i-1)+prime(i+1) = 0 mod 5. a(n) = A000040(i) is in this sequence iff A000040(i-1)+A000040(i+1) = 0 mod 5.
EXAMPLE
a(1) = 5 because prevprime(5) + nextprime(5) = 3 + 7 = 10 = 5 * 2.
a(2) = 11 because prevprime(11) + nextprime(11) = 7 + 13 = 20 = 5 * 4.
a(3) = 19 because prevprime(19) + nextprime(19) = 17 + 23 = 40 = 5 * 8.
a(4) = 41 because prevprime(41) + nextprime(41) = 37 + 43 = 80 = 5 * 16.
MATHEMATICA
Prime@ Select[Range[2, 179], Mod[Prime[ # - 1] + Prime[ # + 1], 5] == 0 &] (* Robert G. Wilson v *)
Select[Partition[Prime[Range[200]], 3, 1], Divisible[#[[1]]+#[[3]], 5]&] [[All, 2]] (* Harvey P. Dale, May 18 2019 *)
CROSSREFS
Sequence in context: A105914 A289530 A106016 * A163419 A337492 A236584
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Jan 01 2006
EXTENSIONS
Corrected and extended by Robert G. Wilson v, Jan 05 2006
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)