

A292530


Primes prime(k) such that neither prime(k) + prime(k1) nor prime(k) + prime(k+1) is divisible by 3.


3



3, 53, 157, 173, 211, 257, 263, 373, 509, 541, 563, 593, 607, 653, 733, 947, 977, 997, 1069, 1103, 1123, 1187, 1223, 1237, 1367, 1459, 1499, 1511, 1543, 1747, 1753, 1759, 1777, 1901, 1907, 1913, 2069, 2179, 2287, 2399, 2411, 2417, 2447, 2677, 2903, 2963, 3061, 3067, 3181, 3203, 3307, 3313, 3511
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OFFSET

1,1


COMMENTS

Prime(k) is the kth prime. It seems to be rare that the sum of two consecutive primes is not divisible by 3. For each prime(k) in this sequence (other than prime(2) = 3), the three numbers prime(k1), prime(k), and prime(k+1) are all of the form 6*x+1 or all of the form 6*x1.
Apart from the first term a(1) = 3 also middle of 3 consecutive primes whose sum is divisible by 3.  Hugo Pfoertner, Aug 29 2020


LINKS

Table of n, a(n) for n=1..53.


EXAMPLE

3 is a term, because 3+2 = 5 and 3+5 = 8; neither 5 nor 8 is divisible by 3.
53 is a term as well, because 53+47 = 100 and 53+59 = 112, and neither 100 nor 112 is divisible by 3.


MAPLE

Primes:= select(isprime, [2, seq(i, i=3..10000, 2)]):
R:= select(k > Primes[k]+Primes[k1] mod 3 <> 0, {$2..nops(Primes)}):
R:= R intersect map(``, R, 1);
Primes[sort(convert(R, list))]; # Robert Israel, Sep 18 2017


MATHEMATICA

Select[Prime@ Range@ 500, NoneTrue[# + {NextPrime[#, 1], NextPrime@ #}, Divisible[#, 3] &] &] (* Michael De Vlieger, Sep 19 2017 *)


PROG

(PARI) isok(p) = isprime(p) && ((p + precprime(p1)) % 3) && ((p + nextprime(p+1)) % 3) \\ Michel Marcus, Sep 18 2017


CROSSREFS

Sequence in context: A106997 A141929 A216042 * A036941 A113612 A215435
Adjacent sequences: A292527 A292528 A292529 * A292531 A292532 A292533


KEYWORD

nonn


AUTHOR

Marc Morgenegg, Sep 18 2017


EXTENSIONS

More terms from Robert Israel, Sep 18 2017


STATUS

approved



