A061068 -id:A061068 - cp's OEIS frontend

A139027 This is to A139026 as A139026 to A139025, see A139025 for details.

1292, 3865, 4666, 8973, 13936, 50339, 57266, 67597, 72316, 85343, 110934, 132941, 147990, 220203, 226652, 270239, 272950, 313361, 366186, 375253, 392090, 409619, 412024, 415237, 469982, 511263, 556808, 635279, 640716, 654559, 711018, 721629

Offset: 1

Zak Seidov, Apr 07 2008

nonn

Notice that a(n)-n is always prime by definition, e.g.,

a(1) - 1 = 1291, a(2) - 2 = 3863, a(3) - 3 = 4663, a(4) - 4 = 8969, etc.

Cf. A000027, A014688, A061068, A139025, A139026, A139028, A139029.

A139028 This is to A139027 as A139027 to A139026, see A139025 for details.

Original entry on oeis.org

270240, 375255, 635282, 1000695, 2039428, 2602013, 3398274, 3748771, 4300120, 4889577, 5643252, 6595775, 8684760, 12489373, 12758734, 15186995, 15557178, 17151151, 17988320, 18564859, 19878764, 20317745, 21560274, 22466983

Offset: 1

Zak Seidov, Apr 07 2008

nonn

Notice that a(n)-n is always prime by definition, e.g.,

a(1) - 1 = 270239, a(2) - 2 = 375253, a(3) - 3 = 635279, a(4) - 4 = 1000691, etc.

Cf. A000027, A014688, A061068, A139025, A139026, A139027, A139029.

A139029 This is to A139028 as A139028 to A139027, see A139025 for details.

Original entry on oeis.org

43448724, 59672019, 102128690, 113904945, 145135734, 169755139

Offset: 1

Zak Seidov, Apr 07 2008

Notice that a(n)-n is always prime by definition, e.g.,

a(1) - 1 = 43448723, a(2) - 2 = 59672017, a(3) - 3 = 102128687, a(4) - 4 = 113904941, etc.

Cf. A000027, A014688, A061068, A139025, A139026, A139027, A139028.

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]

A071328 Smallest prime q such that q - prime(n) >= n.

Original entry on oeis.org

3, 5, 11, 11, 17, 19, 29, 29, 37, 41, 43, 53, 59, 59, 67, 71, 79, 79, 89, 97, 97, 101, 107, 113, 127, 127, 131, 137, 139, 149, 163, 163, 173, 173, 191, 191, 197, 211, 211, 223, 223, 223, 239, 239, 251, 251, 263, 271, 277, 281, 293, 293, 307, 307

Offset: 1

Reinhard Zumkeller, May 19 2002

nonn

a(n) = A007918(n + A000040(n));

a(n) = A071329(n) iff a(n) = A061068(k) for some k.

			a(10) = A007918(10 + A000040(10)) = A007918(10 + 29)= A007918(39) = 41;
a(6) = A007918(6 + A000040(6)) = A007918(6 + 13)= A007918(19) = 19 = A071329(6) = A061068(4).

Robert Israel, Table of n, a(n) for n = 1..10000

seq(nextprime(n + ithprime(n)-1),n=1..100); # Robert Israel, Jul 12 2019

A078917 Primes of the form prime(k) + 2*k.

Original entry on oeis.org

7, 11, 31, 41, 53, 61, 67, 71, 97, 137, 157, 163, 167, 173, 223, 239, 277, 281, 347, 359, 367, 383, 401, 433, 439, 443, 449, 503, 521, 569, 601, 643, 673, 761, 769, 809, 821, 829, 877, 883, 941, 953, 1031, 1063, 1093, 1109, 1153, 1163, 1217, 1223, 1277, 1307

Offset: 1

Reinhard Zumkeller, Dec 13 2002

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Cf. A078916, A061068, A000040.

[a: n in [1..200] | IsPrime(a) where a is NthPrime(n)+2*n ]; // Vincenzo Librandi, Dec 09 2011

Select[Table[Prime[n]+2n,{n,68000}],PrimeQ] (* Vincenzo Librandi, Dec 09 2011 *)

A231326 Primes p such that p - 2*k is also prime, where p is k-th prime.

Original entry on oeis.org

17, 19, 23, 37, 47, 67, 71, 73, 83, 89, 97, 113, 131, 137, 139, 149, 151, 157, 167, 179, 181, 197, 199, 223, 233, 263, 307, 331, 353, 379, 397, 419, 421, 439, 443, 457, 461, 463, 503, 557, 587, 613, 631, 641, 643, 659, 661, 677, 701, 719, 743, 761, 773, 839, 863

Offset: 1

K. D. Bajpai, Nov 07 2013

nonn

			a(2)= 19 which is 8th prime. prime(8)-2*8= 19-16= 3 which is also prime.
a(6)= 67 which is 19th prime. prime(19)-2*19= 67-38= 29 which is also prime.

K. D. Bajpai, Table of n, a(n) for n = 1..5200

Cf. A061068 (primes: prime(m) plus its subscript).
Cf. A064402 (numbers n: prime(n)+n is prime).
Cf. A227420 (primes: p - pi(p) is also prime).
Cf. A231232 (primes: prime(k)+2*k is also prime).

KD := proc() local a,b; a:= ithprime(n); b := a-2*n; if isprime(b) then RETURN (a); fi;end: seq(KD(),n=1..500);

TK = Select[Table[{Prime[n], Prime[n] - 2*n}, {n, 200}], PrimeQ[#[[2]]] &]; Transpose[TK][[1]]

A231506 Primes p such that p + 3k and p - 3k, both are primes, where p is k-th prime.

Original entry on oeis.org

7, 13, 19, 53, 71, 101, 107, 139, 173, 199, 223, 229, 281, 293, 397, 463, 557, 569, 673, 787, 809, 839, 953, 1013, 1283, 1451, 1559, 1657, 1861, 1871, 1877, 1949, 1987, 1997, 2213, 2311, 2347, 2357, 2377, 2503, 2543, 2551, 2593, 2633, 2837, 2851, 2939, 2999, 3041

Offset: 1

K. D. Bajpai, Nov 09 2013

nonn

			a(7)= 107 which is 28th prime. prime(28)-3*28= 107-84= 23: prime(28)+3*28= 107+84= 191: 23 and 191 both are primes.
a(9)= 173 which is 40th prime. prime(40)-3*40= 173-120= 53: prime(40)+3*40= 173+120= 293: 53 and 293 both are primes.

K. D. Bajpai, Table of n, a(n) for n = 1..5200

Cf. A061068 (primes: prime(m) plus its subscript).
Cf. A064402 (numbers n: prime(n)+n is prime).
Cf. A231232 (primes p : p+2*k is also primes).
Cf. A231383 (primes p : p+3*k is also primes).

KD := proc() local a,b,d;  a:= ithprime(n); b:= abs(a-3*n);d:=(a+3*n); if isprime(b) and  isprime(d) then RETURN (a); fi; end: seq(KD(), n=1..500);

A071329 Largest prime q such that q - prime(n) <= n.

Original entry on oeis.org

3, 5, 7, 11, 13, 19, 23, 23, 31, 37, 41, 47, 53, 53, 61, 67, 73, 79, 83, 89, 89, 101, 103, 113, 113, 127, 127, 131, 137, 139, 157, 163, 167, 173, 181, 181, 193, 199, 199, 211, 211, 223, 233, 233, 241, 241, 257, 271, 271, 277, 283, 283, 293, 293

Offset: 1

Reinhard Zumkeller, May 19 2002

nonn

a(n) = A007917(n + A000040(n));

a(n) = A071328(n) iff a(n) = A061068(k) for some k.

			a(10) = A007917(10 + A000040(10)) = A007917(10 + 29)= A007917(39) = 37;
a(6) = A007917(6 + A000040(6)) = A007917(6 + 13)= A007917(19) = 19 = A071328(6) = A061068(4).

With[{prs=Prime[Range[100]]},Table[Last[Select[prs,(#-prs[[n]]<=n)&]],{n,60}]] (* Harvey P. Dale, May 11 2012 *)

A081717 Primes prime(j) such that prime(j) + j is composite.

Original entry on oeis.org

5, 11, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 67, 71, 73, 83, 97, 103, 107, 109, 113, 127, 137, 149, 151, 157, 163, 167, 173, 179, 191, 193, 197, 199, 211, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 331, 337, 347

Offset: 1

Labos Elemer, Apr 02 2003

nonn

			127 is the 31st prime and 127+31 = 158 is composite.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A061067, A061068.

Do[s=Prime[n]+n; If[ !PrimeQ[s], Print[Prime[n]]], {n, 1, 100}]

cp's OEIS Frontend

A139027 This is to A139026 as A139026 to A139025, see A139025 for details.

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A139028 This is to A139027 as A139027 to A139026, see A139025 for details.

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A139029 This is to A139028 as A139028 to A139027, see A139025 for details.

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

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A071328 Smallest prime q such that q - prime(n) >= n.

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Maple

A078917 Primes of the form prime(k) + 2*k.

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Magma

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A231326 Primes p such that p - 2*k is also prime, where p is k-th prime.

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A231506 Primes p such that p + 3*k and p - 3*k, both are primes, where p is k-th prime.

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Maple

A071329 Largest prime q such that q - prime(n) <= n.

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Mathematica

A081717 Primes prime(j) such that prime(j) + j is composite.

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A231506 Primes p such that p + 3k and p - 3k, both are primes, where p is k-th prime.