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A292530 Primes prime(k) such that neither prime(k) + prime(k-1) 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Prime(k) is the k-th 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(k-1), prime(k), and prime(k+1) are all of the form 6*x+1 or all of the form 6*x-1.

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[k-1] 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(p-1)) % 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

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Last modified January 16 18:17 EST 2022. Contains 350376 sequences. (Running on oeis4.)