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A339944 Let N(p,i) denote the result of applying "nextprime" i times to p; a(n) = smallest prime p such that N(p,4) - p = 2*n, or 0 if no such prime exists. 2
0, 0, 0, 0, 3, 5, 17, 13, 19, 47, 79, 73, 113, 109, 193, 317, 313, 521, 503, 523, 887, 1499, 1231, 1319, 1373, 1321, 1307, 3947, 2473, 2143, 2477, 7369, 5573, 5939, 9967, 16111, 18587, 20773, 18593, 31883, 17209, 19597, 24251, 19609, 25471, 31397, 44389, 18803, 38459, 38461, 66191, 69557, 103183 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

This sequence is the fourth row of A337767.

From Robert G. Wilson v, Dec 30 2020: (Start)

a(n) > 0 and that there are multiple instances for some k where (p_(k+4) - p_k)/2 = n. This sequence only cites the first such occurrence.

n:

5:   3.

6:   5,  7,  11,  97, 101, 1481, 1867, 3457, 5647, 15727, 16057, 16061, ... ,

7:  17, 29,  59, 227, 269, 1277, 1289, 1607, 2129,  2789,  3527,  3917, ... ,

8:  13, 31,  37,  67, 223, 1087, 1291, 1423, 1483,  1597,  1861,  1987, ... ,

9:  19, 23,  41,  43,  53,   61,   71,   89,  149,   163,   179,   181, ... ,

10: 47, 83, 131, 137, 173,  191,  251,  257,  347,   419,   443,   557, ... ,

etc.

(End)

LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..342

EXAMPLE

a(1) = 3. This represents the beginning of the run of primes {3, 5, 7, 11, 13}. (13 - 3)/2 = 5 and it is the only prime to do so.

a(2) = 5. This represents the beginning of the run of primes {5, 7, 11, 13, 17}. (17 - 5)/2 = 6 and it is the first prime to do so. Others are 7, 11, 97, 101, etc.

a(3) = 17. This represents the beginning of the run of primes {17, 19, 23, 29, 31}. (31 - 17)/2 = 7 and it is the first prime to do so. Others are 29, 59, 227, 269, etc.

MATHEMATICA

p = 3; q = 5; r = 7; s = 11; t = 13; tt[_] := 0; While[p < 450000, d = (t - p)/2; If[ tt[d] == 0, tt[d] = p]; {p, q, r, s, t} = {q, r, s, t, NextPrime@ t}]; tt@# & /@ Range@ 75 (* Robert G. Wilson v, Dec 30 2020 *)

CROSSREFS

Cf. A337767, A000230, A144103, A339943.

Sequence in context: A242104 A158895 A085418 * A292008 A139427 A191051

Adjacent sequences:  A339941 A339942 A339943 * A339945 A339946 A339947

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Dec 23 2020

STATUS

approved

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Last modified January 21 22:08 EST 2022. Contains 350480 sequences. (Running on oeis4.)