A094105 -id:A094105 - cp's OEIS frontend

A175914 Primes p such that p+2*q is prime, where q is the prime after p.

3, 5, 7, 11, 13, 41, 43, 59, 89, 101, 103, 113, 127, 179, 181, 191, 193, 223, 241, 269, 277, 293, 307, 311, 313, 337, 359, 421, 431, 479, 491, 521, 599, 613, 631, 673, 773, 787, 821, 823, 863, 881, 883, 907, 911, 919, 929, 937, 953, 967, 1019, 1021, 1039, 1061, 1109, 1151, 1171

Offset: 1

Zak Seidov, Dec 05 2010

nonn

A174915 gives lesser of twin primes in this sequence.

Values of p+2*q are in A094105. [Zak Seidov, Sep 07 2012]

			3 and 5 are consecutive primes, and 3+2*5 = 13 is prime. Hence 3 is in the sequence.
59 and 61 are consecutive primes, and 59+2*61 = 181 is prime. Hence 59 is in the sequence.

Zak Seidov, Table of n, a(n) for n = 1..1000

Cf. A094105, A114262, A174915, A001359.

[p: p in PrimesUpTo(1200) | IsPrime(p+2*NextPrime(p))]; // Klaus Brockhaus, Dec 06 2010

p = 3; Reap[Do[q = NextPrime[p]; If[PrimeQ[p + 2 q], Sow[p]]; p = q, {10^3}]][[2, 1]] (* Zak Seidov, Oct 14 2012 *)

A094104 Primes of the form 2*prime(n) + prime(n+1).

Original entry on oeis.org

7, 11, 17, 43, 53, 61, 89, 179, 241, 313, 331, 353, 449, 593, 673, 683, 691, 719, 733, 809, 859, 1021, 1051, 1237, 1259, 1321, 1481, 1709, 1741, 1933, 1979, 2083, 2111, 2137, 2221, 2237, 2311, 2333, 2371, 2473, 2531, 2741, 2767, 2957, 3163, 3469, 3643

Offset: 1

Giovanni Teofilatto, May 02 2004

No intersection with A094105 (Primes of the form prime(m) + 2*prime(m+1)). In general, an integer of the form 2*prime(m) + prime(m+1) cannot be of the form prime(n) + 2*prime(n+1). - Zak Seidov, May 03 2014

			a(7) = 2*29 + 31 = 89.

Zak Seidov, Table of n, a(n) for n = 1..1000

Cf. A094105.

f[n_] := (2Prime[n] + Prime[n + 1]); f[ # ] & /@ Select[Range[160], PrimeQ[f[ # ]] &] (* Robert G. Wilson v *)
Select[2#[[1]]+#[[2]]&/@Partition[Prime[Range[300]],2,1],PrimeQ] (* Harvey P. Dale, Jul 19 2022 *)

q=2;forprime(p=3,1300,if(isprime(r=2*q+p),print1(r,","));q=p)

Corrected and extended by Klaus Brockhaus and Robert G. Wilson v, May 07 2004

A241945 Indices n where both prime(n) + 2prime(n+1) and 2prime(n) + prime(n+1) are primes.

Original entry on oeis.org

2, 3, 6, 17, 27, 30, 48, 53, 57, 68, 94, 137, 138, 143, 156, 157, 248, 259, 269, 289, 296, 316, 360, 369, 402, 425, 429, 430, 432, 446, 474, 500, 522, 580, 596, 631, 656, 760, 777, 810, 828, 875, 906, 951, 994, 1154, 1163, 1233, 1273, 1338, 1346, 1352, 1378, 1381, 1385, 1391, 1402, 1422, 1436, 1495, 1552, 1602

Offset: 1

Zak Seidov, May 03 2014

nonn

			n=2 is in the sequence because 3 + 2*5 = 13 and 5 + 2*3 = 11 are primes.
n=3 is in the sequence because 5 + 2*7 = 19 and 7 + 2*5 = 17 are primes.
n=6 is in the sequence because 17 + 2*13 = 43 and 13 + 2*17 = 47 are primes.

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

Cf. A094104 (primes of form 2*p + q), A094105 (primes of form p + 2*q).

Cf. A181848, A186169, A215684.

isok(n) = my(p=prime(n), q=nextprime(p+1)); isprime(p+2*q) && isprime(2*p+q); \\ Michel Marcus, Jan 06 2019

A215808 Primes of the form 2*prime(k) - prime(k+1).

Original entry on oeis.org

3, 3, 17, 41, 47, 67, 151, 167, 199, 227, 251, 257, 347, 367, 557, 587, 601, 607, 641, 647, 727, 941, 971, 1051, 1091, 1097, 1117, 1181, 1217, 1277, 1361, 1427, 1447, 1447, 1487, 1487, 1499, 1607, 1697, 1741, 1747, 1741, 1777, 1877, 1901, 2087, 2143, 2281

Offset: 1

Zak Seidov, Sep 06 2012

nonn

Corresponding values of k: 3, 4, 9, 15, 16, 21, 37, 40, 47, 51, 55, 56, 71, 74, 103 (A216075).

			k=3: 2*5-7=3, k=4: 2*7-11=3, k=9: 2*23-29=17.

Zak Seidov, Table of n, a(n) for n = 1..1000

Cf. A062234, A085704, A094104, A094105, A216075.

pr=Prime[Range[1000]]; s=Select[2*Most[pr]-Rest[pr],PrimeQ]
Select[2#[[1]]-#[[2]]&/@Partition[Prime[Range[500]],2,1],PrimeQ] (* Harvey P. Dale, Feb 25 2017 *)

A364411 a(n) = prime(n) + 2*prime(n+1).

Original entry on oeis.org

8, 13, 19, 29, 37, 47, 55, 65, 81, 91, 105, 119, 127, 137, 153, 171, 181, 195, 209, 217, 231, 245, 261, 283, 299, 307, 317, 325, 335, 367, 389, 405, 415, 437, 451, 465, 483, 497, 513, 531, 541, 563, 577, 587, 595, 621, 657, 677, 685, 695, 711, 721, 743, 765, 783

Offset: 1

Paul Curtz, Jul 23 2023

All terms > 8 are odd.

Paolo Xausa, Table of n, a(n) for n = 1..10000

Cf. A000040, A001043, A062234, A094105, A100484, A191472 (first differences), A210497.

ListConvolve[{2,1},Prime[Range[100]]] (* Paolo Xausa, Nov 02 2023 *)

a(n) = a(n-1) + A191472(n-1).
a(n) = A000040(n) + A100484(n+1).
a(n) = A000040(n+1) + A001043(n).

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A175914 Primes p such that p+2*q is prime, where q is the prime after p.

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A094104 Primes of the form 2*prime(n) + prime(n+1).

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A241945 Indices n where both prime(n) + 2*prime(n+1) and 2*prime(n) + prime(n+1) are primes.

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A215808 Primes of the form 2*prime(k) - prime(k+1).

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A364411 a(n) = prime(n) + 2*prime(n+1).

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A241945 Indices n where both prime(n) + 2prime(n+1) and 2prime(n) + prime(n+1) are primes.