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A112859 Primes such that the sum of the predecessor and successor primes is divisible by 29. 18
149, 433, 463, 491, 839, 907, 929, 953, 1217, 1451, 1741, 2789, 2957, 3853, 3917, 4493, 4639, 4957, 5021, 5167, 5227, 5569, 6353, 6673, 6733, 6823, 7219, 7481, 7573, 7649, 7919, 8293, 8443, 8699, 9281, 9421, 9743, 9923, 10151, 10211, 10709, 11161 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
There is a trivial analogy to every prime beyond 3, but mod 2. A112681 is analogous to this, but mod 3. A112731 is analogous to this, but mod 7. A112789 is analogous to this, but mod 11.
LINKS
FORMULA
a(n) = prime(i) is in this sequence iff prime(i-1)+prime(i+1) = 0 mod 29. a(n) = A000040(i) is in this sequence iff A000040(i-1)+A000040(i+1) = 0 mod 29.
EXAMPLE
a(1) = 149 because prevprime(149) + nextprime(149) = 139 + 151 = 290 = 29 * 10.
a(2) = 433 because prevprime(433) + nextprime(433) = 431 + 439 = 870 = 29 * 30.
a(3) = 463 because prevprime(463) + nextprime(463) = 461 + 467 = 928 = 29 * 32.
a(4) = 491 because prevprime(491) + nextprime(491) = 487 + 499 = 986 = 29 * 34.
MAPLE
Primes:= select(isprime, [seq(i, i=3..20000, 2)]):
R:= select(t -> Primes[t-1]+Primes[t+1] mod 29 = 0, [$2..nops(Primes)-1]):
Primes[R]; # Robert Israel, May 02 2017
MATHEMATICA
Prime@ Select[Range[2, 1372], Mod[Prime[ # - 1] + Prime[ # + 1], 29] == 0 &] (* Robert G. Wilson v, Jan 05 2006 *)
CROSSREFS
Sequence in context: A142359 A185692 A216312 * A141980 A023290 A142629
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Jan 01 2006
EXTENSIONS
More terms from Robert G. Wilson v, Jan 05 2006
STATUS
approved

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Last modified March 28 12:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)