login
A112859
Primes such that the sum of the predecessor and successor primes is divisible by 29.
16
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
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 *)
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Jan 01 2006
EXTENSIONS
More terms from Robert G. Wilson v, Jan 05 2006
STATUS
approved