A071195 -id:A071195 - cp's OEIS frontend

A071198 Impossible primes in A071195. These primes are not terminal primes of shortest consecutive prime sequences initiated with n-th prime and providing prime-sum.

2, 5, 7, 19, 43, 53, 59, 67, 83, 101, 103, 109, 163, 179, 181, 191, 193, 199, 229, 233, 241, 257, 263, 271, 277, 313, 337, 347, 367, 373, 431, 433, 449, 467, 491, 499, 521, 541, 547, 571, 587, 607, 613, 619, 643, 659, 683, 701

Offset: 1

Labos Elemer, May 16 2002

nonn

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Cf. A071194, A071195, A071196, A071197.

Complement[Prime@ Range@ PrimePi@ Last@ #, #] &@ Prime@ Table[k = 1; While[! PrimeQ@ Total@ Prime@ Range[n, n + k], k++]; n + k, {n, 125}] (* Michael De Vlieger, Jul 18 2017 *)

A071197 Possible prime values in A071195.

Original entry on oeis.org

3, 11, 13, 17, 23, 29, 31, 37, 41, 47, 61, 71, 73, 79, 89, 97, 107, 113, 127, 131, 137, 139, 149, 151, 157, 167, 173, 197, 211, 223, 227, 239, 251, 269, 281, 283, 293, 307, 311, 317, 331, 349, 353, 359, 379, 383, 389, 397, 401, 409, 419, 421, 439, 443, 457

Offset: 1

Labos Elemer, May 16 2002

nonn

Cf. A071194-A071198.

A071194 Length (>1) of shortest sequence of consecutive primes starting with prime(n) whose sum is also prime, or -1 if no such sequence exists.

Original entry on oeis.org

2, 9, 3, 3, 3, 5, 3, 3, 3, 3, 3, 9, 3, 5, 7, 3, 5, 3, 3, 3, 5, 3, 3, 7, 7, 3, 7, 5, 3, 5, 5, 9, 5, 3, 3, 5, 3, 3, 11, 9, 5, 21, 5, 9, 3, 9, 3, 5, 55, 3, 7, 27, 9, 27, 7, 5, 5, 3, 9, 3, 3, 3, 5, 3, 7, 7, 11, 3, 3, 3, 5, 5, 7, 7, 3, 5, 3, 9, 3, 3, 5, 11, 3, 5, 47, 5, 3, 3, 5, 3, 3, 5, 7, 3, 3, 7, 3, 5, 5, 5, 3

Offset: 1

Labos Elemer, May 16 2002

nonn

			For n=1, start-prime = prime(1) = 2, 2+3=5 is prime, length=2, so a(1)=2;
for n=2, start-prime = prime(2) = 3, 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 = 127 is prime, length=9, all shorter partial sums are composite, so a(2)=9;
for n=160, prime(160) = 941, 941 + ... + 1609 = 121123 is prime, a(160)=95.

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

Cf. A071195, A071196, A071197, A071198.

Table[k = 2; While[CompositeQ@ Total@ Prime@ Range[n, n + k], k++]; k + 2 Boole[EvenQ@ k] - 1, {n, 120}] (* Michael De Vlieger, Jan 01 2017 *)

a(n,p=prime(n))=my(q=p,t=2); while(!isprime(p+=q=nextprime(q+1)),t++);t
apply(p->a(0,p), primes(30)) \\ Charles R Greathouse IV, Jun 16 2015

Escape clause added by N. J. A. Sloane, Nov 17 2020

A071196 The sum of the sequence starting with prime(n) and having prime sum defined in A071194, or -1 if no such sequence exists.

Original entry on oeis.org

5, 127, 23, 31, 41, 101, 59, 71, 83, 97, 109, 479, 131, 263, 431, 173, 331, 199, 211, 223, 421, 251, 269, 719, 757, 311, 827, 587, 349, 647, 683, 1367, 733, 439, 457, 811, 487, 503, 2141, 1747, 941, 5009, 991, 1951, 607, 2053, 661, 1151, 21139, 701, 1753

Offset: 1

Labos Elemer, May 16 2002

			n=25: prime(25)=97, sum=97+101+103+107+109+113+127=757=a(25), prime; shorter (length>1) partial sums are composite: {97,198,301,408,517,630,757}.

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, Colored logarithmic scatterplot of the first 10000 terms (where the color is function of A071194(n))

Cf. A000040, A071194, A071195, A071197, A071198.

Table[sm = Prime[k] + Prime[k + 1]; g = 1; While[ ! PrimeQ[sm], g++; sm = sm + Prime[k + g]]; sm, {k, 1, 51}] (* Lei Zhou, Dec 02 2005 *)

{ forprime (p=2, prime(51), s=p; forprime (q=p+1, oo, if (isprime(s+=q), print1 (s", "); break))) } \\ Rémy Sigrist, Nov 17 2020

Edited and escape clause added by N. J. A. Sloane, Nov 17 2020~

cp's OEIS Frontend

A071198 Impossible primes in A071195. These primes are not terminal primes of shortest consecutive prime sequences initiated with n-th prime and providing prime-sum.

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A071197 Possible prime values in A071195.

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A071194 Length (>1) of shortest sequence of consecutive primes starting with prime(n) whose sum is also prime, or -1 if no such sequence exists.

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A071196 The sum of the sequence starting with prime(n) and having prime sum defined in A071194, or -1 if no such sequence exists.

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