A152468 -id:A152468 - cp's OEIS frontend

A288041 Numbers k such that prime(k) + prime(k+1) + ... + prime(k+4) is prime.

3, 4, 5, 6, 8, 10, 11, 14, 16, 17, 19, 21, 22, 28, 29, 30, 31, 33, 35, 36, 37, 38, 41, 43, 47, 48, 50, 56, 57, 63, 64, 70, 71, 72, 75, 76, 79, 80, 81, 84, 86, 87, 89, 91, 92, 98, 99, 100, 102, 104, 105, 106, 109, 112, 114, 119, 123, 125, 134, 140, 141, 142, 146, 148, 149, 150

Offset: 1

Zak Seidov, Jun 04 2017

nonn

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A000720 (PrimePi), A072225 (numbers n such that prime(n) + prime(n+1) + prime(n+2) is prime), A073681 (smallest of three consecutive primes whose sum is a prime), A152468 (smallest of five consecutive primes whose sum is a prime).

With[{nn = 154}, Function[s, Select[Range[nn - 4], PrimeQ@ Total@ Take[s, {#, # + 4}] &]]@ Prime@ Range@ nn] (* Michael De Vlieger, Jun 06 2017 *)
Position[Total/@Partition[Prime[Range[200]],5,1],?(PrimeQ[#]&)]//Flatten (* _Harvey P. Dale, Sep 09 2024 *)

list(lim)=my(v=List(),u=primes(5),n=1); forprime(p=13,, if(n++>lim, break); u=concat(u[2..5],p); if(isprime(vecsum(u)), listput(v,n))); Vec(v) \\ Charles R Greathouse IV, Jun 10 2017

a(n) = pi(A152468(n)) = A000720(A152468(n)).

A228198 Smallest of five consecutive primes whose sum is not a prime.

Original entry on oeis.org

2, 3, 17, 23, 37, 41, 47, 61, 71, 83, 89, 97, 101, 103, 131, 139, 167, 173, 181, 193, 197, 199, 227, 233, 239, 241, 251, 257, 271, 277, 281, 283, 293, 313, 317, 331, 337, 347, 367, 373, 389, 397, 421, 431, 439, 457, 463, 487, 491, 499, 503, 509, 547, 563, 587, 593

Offset: 1

Vincenzo Librandi, Aug 20 2013

nonn

			47 is in the sequence because 47+53+59+61+67 = 287 and 287 is not a prime.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A000040, A152468.

[NthPrime(n): n in [1..120] | not IsPrime(&+[NthPrime(n+s): s in [0..4]])];

Transpose[Select[Partition[Prime[Range[150]], 5, 1], ! PrimeQ[Total[#]] &]][[1]]
Prime[Select[Range[150], ! PrimeQ[Sum[Prime[# + i], {i, 0, 4}]] &]] (* Bruno Berselli, Aug 21 2013 *)

A229059 Smallest of 13 consecutive primes whose sum is a prime.

Original entry on oeis.org

29, 41, 47, 61, 71, 89, 97, 103, 107, 131, 139, 149, 193, 211, 241, 263, 277, 293, 311, 313, 349, 353, 379, 383, 397, 401, 419, 443, 461, 491, 521, 557, 593, 599, 631, 647, 677, 739, 761, 809, 827, 877, 983, 1013, 1039, 1061, 1109, 1117, 1171, 1193, 1201

Offset: 1

Vincenzo Librandi, Sep 13 2013

nonn

			a(1)=29 since 29+31+37+41+43+47+53+59+61+67+71+73+79=691 is a prime.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A073681, A152468, A180948, A189571, A180950, A226380.

[NthPrime(n): n in [1..200] | IsPrime(&+[NthPrime(n+s): s in [0..12]])];

Transpose[Select[Partition[Prime[Range[250]], 13, 1], PrimeQ[Total[#]]&]][[1]]

cp's OEIS Frontend

A288041 Numbers k such that prime(k) + prime(k+1) + ... + prime(k+4) is prime.

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A228198 Smallest of five consecutive primes whose sum is not a prime.

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A229059 Smallest of 13 consecutive primes whose sum is a prime.

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Magma

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