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A339943 Let N(p,i) denote the result of applying "nextprime" i times to p; a(n) = smallest prime p such that N(p,3) - p = 2*n, or -1 if no such prime exists. 2
-1, -1, -1, 3, 7, 17, 23, 43, 79, 107, 109, 113, 197, 199, 317, 509, 523, 773, 1823, 1237, 1319, 3119, 1321, 2473, 2153, 4159, 2477, 6491, 5581, 7351, 9551, 9973, 18803, 18593, 24247, 30559, 31883, 33211, 19603, 66191, 37699, 31393, 83117, 43801, 107351, 107357, 69499, 38461, 130859 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

This sequence is the third row of A337767.a(n) > 0 and that there are multiple instances for some k where (p_(k+3) - p_k)/2 - 3 = n.

This sequence only cites the first such occurrence.

n:

4:    3,   5,  11, 101, 191, 821, 1481, 1871, 2081, 3251, 3461, 5651, ...,

5:    7,  13,  37,  97, 103, 223,  307,  457,  853,  877, 1087, 1297, ...,

6:   17,  19,  29,  31,  41,  59,   61,   67,   71,  127,  227,  229, ...,

7:   23,  47,  53,  89, 137, 149,  167,  179,  257,  263,  419,  449, ...,

8:   43,  73, 151, 157, 163, 181,  277,  337,  367,  373,  433,  487, ...,

9:   79,  83, 131, 139, 173, 193,  211,  233,  239,  251,  331,  349, ...,

10: 107, 293, 311, 353, 359, 389,  401,  479,  503,  653,  719,  839, ...,

etc.

LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..345

EXAMPLE

a(4) = 3. This represents the beginning of the run of primes {3, 5, 7, 11}. (11 - 3)/2 = 4 and it is the first prime to do so. Others are 5, 11, 101, 191, etc.;

a(5) = 7. This represents the beginning of the run of primes {7, 11, 13, 17}. (17 - 7)/2 = 5 and it is the first prime to do so. Others are 13, 37, 97, 103, etc.;

a(6) = 17. This represents the beginning of the run of primes {17, 19, 23 & 29}. (29 - 17)/2 = 6 and it is the first prime to do so. Others are 19, 29, 31, 41, etc.

MATHEMATICA

p = 3; q = 5; r = 7; s = 11; tt[_] := 0; While[p < 250000, d = (s - p)/2; If[ tt[d] == 0, tt[d] = p]; {p, q, r, s} = {q, r, s, NextPrime@ s}]; tt@# & /@ Range@ 75

CROSSREFS

Cf. A000230, A001223, A144103, A337767, A339944.

Sequence in context: A097958 A118940 A127175 * A127355 A079470 A056815

Adjacent sequences:  A339940 A339941 A339942 * A339944 A339945 A339946

KEYWORD

sign

AUTHOR

Robert G. Wilson v, Dec 23 2020

STATUS

approved

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Last modified January 20 21:46 EST 2022. Contains 350472 sequences. (Running on oeis4.)