A076299 -id:A076299 - cp's OEIS frontend

A076297 Numbers k such that prime(k) + s*k is prime, s=2.

2, 3, 7, 9, 11, 12, 13, 14, 18, 24, 27, 28, 29, 30, 36, 38, 43, 44, 53, 54, 55, 57, 60, 63, 64, 65, 66, 72, 74, 80, 84, 90, 93, 102, 103, 108, 110, 111, 117, 118, 125, 126, 135, 138, 141, 143, 148, 150, 155, 156, 162, 165, 171, 174, 180, 183, 186, 188, 190, 198

Offset: 1

Zak Seidov, Oct 05 2002

nonn

See also A064402 (s=1), A076298 (s=3), A076299 (s=4), A076300 (s=5).

			3 is OK because p(3) + 2*3 = 5 + 6 = 11 is prime.

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A064402, A076298, A076299, A076300.

[n: n in [0..500]| IsPrime(NthPrime(n) +2*n)]; // G. C. Greubel, May 04 2018

Select[Range[200],PrimeQ[Prime[#]+2#]&] (* Harvey P. Dale, Sep 01 2015 *)

select(x->isprime(x), vector(500, n, prime(n) + 2*n), 1) \\ G. C. Greubel, May 04 2018

A076300 Numbers k such that prime(k) + s*k is prime, s=5.

Original entry on oeis.org

1, 2, 6, 8, 10, 12, 14, 18, 30, 36, 38, 40, 48, 50, 52, 54, 64, 66, 68, 72, 74, 78, 80, 84, 96, 110, 118, 120, 122, 124, 134, 142, 148, 150, 154, 160, 178, 184, 186, 188, 198, 204, 210, 214, 220, 224, 228, 238, 240, 242, 246, 250, 252, 254, 258, 260, 268, 270

Offset: 1

Zak Seidov, Oct 05 2002

nonn

			2 is in the sequence because p(2) + 5*2 = 3 + 10 = 13 is prime.

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A064402 (s=1), A076297 (s=2), A076298 (s=3), A076299 (s=4).

[n: n in [0..500]| IsPrime(NthPrime(n) +5*n)]; // Vincenzo Librandi, Apr 06 2011

Select[Range[300],PrimeQ[Prime[#]+5#]&] (* Harvey P. Dale, Nov 27 2013 *)

select(x->isprime(x), vector(500, n, prime(n) + 5*n), 1) \\ Michel Marcus, Jan 15 2015

isok(n) = isprime(prime(n) + 5*n); \\ Michel Marcus, May 05 2018

A076298 Numbers k such that prime(k) + s*k is prime, s=3.

Original entry on oeis.org

1, 4, 6, 8, 10, 12, 16, 20, 26, 28, 32, 34, 38, 40, 42, 46, 48, 50, 56, 60, 62, 64, 68, 78, 86, 90, 94, 102, 104, 120, 122, 128, 130, 138, 140, 144, 146, 148, 162, 166, 170, 180, 182, 186, 190, 200, 204, 208, 214, 230, 238, 244, 246, 250, 252, 254, 260, 270, 282

Offset: 1

Zak Seidov, Oct 05 2002

nonn

See also A064402 (s=1), A076297 (s=2), A076299 (s=4), A076300 (s=5).

			4 is OK because p(4) + 3*4 = 7 + 12 = 19 is prime.

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A064402, A076297, A076299, A076300.

[n: n in [0..500]| IsPrime(NthPrime(n) +3*n)]; // G. C. Greubel, May 04 2018

Select[Range[300],PrimeQ[3#+Prime[#]]&] (* Harvey P. Dale, Sep 06 2012 *)

select(x->isprime(x), vector(500, n, prime(n) + 3*n), 1) \\ G. C. Greubel, May 04 2018

A186102 Smallest prime p such that p == n (mod prime(n)).

Original entry on oeis.org

3, 2, 3, 11, 5, 19, 7, 103, 101, 97, 11, 197, 13, 229, 109, 281, 17, 79, 19, 233, 167, 101, 23, 113, 607, 127, 233, 349, 29, 821, 31, 163, 307, 173, 631, 1093, 37, 853, 373, 1597, 41, 223, 43, 1009, 439, 643, 47, 271, 503, 2111, 983, 769, 53, 1811, 569, 2423

Offset: 1

Zak Seidov, Feb 12 2011

nonn

a(n) = n iff n is prime.

			Eighth prime is 19, and 103 is the smallest prime p such that p mod 19 is 8. Therefore a(8) = 103.

Zak Seidov, Table of n, a(n) for n = 1..10000

Cf. A061067, A061068, A064402, A076297, A076298, A076299, A076300.

Cf. A000040, A260416.

a186102 n = f a000040_list where
   f (q:qs) = if (q - n) `mod` (a000040 n) == 0 then q else f qs
-- Reinhard Zumkeller, Aug 21 2015

Aux:=function(n); q:=NthPrime(n); p:=2; while p mod q ne n do p:=NextPrime(p); end while; return p; end function; [ Aux(n): n in [1..70] ]; // Klaus Brockhaus, Feb 12 2011

k=200;Table[p=Prime[n];m=n;While[!PrimeQ[m],m=m+p];m,{n,k}]; (* For the first k terms. Zak Seidov, Dec 13 2013 *)
Flatten[With[{prs=Prime[Range[500]]},Table[Select[prs,Mod[#,Prime[n]] == n&,1],{n,60}]]] (* Harvey P. Dale, Mar 30 2012 *)

def A186102(n): np = nth_prime(n); return next(p for p in Primes() if p % np == n) # [D. S. McNeil, Feb 13 2011]

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A076297 Numbers k such that prime(k) + s*k is prime, s=2.

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A076300 Numbers k such that prime(k) + s*k is prime, s=5.

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A076298 Numbers k such that prime(k) + s*k is prime, s=3.

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A186102 Smallest prime p such that p == n (mod prime(n)).

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