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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
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 *)
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Jan 01 2006
EXTENSIONS
Corrected and extended by Robert G. Wilson v, Jan 05 2006
STATUS
approved