A216290 Values of k such that 100k+1, 100k+3, 100k+7, 100k+9, 100k+13, 100k+27 are consecutive primes.

1, 40426, 85405, 191434, 209896, 369853, 598774, 652468, 719986, 797116, 1028749, 1097752, 1874920, 1892458, 1898398, 2041768, 2389861, 2390344, 2462944, 2651881, 3182338, 3230953, 3314239, 3531106, 3717985, 3734347, 3898165, 3940438, 3994096, 4075846, 4523548, 4870279, 5176018

Offset

1,2

Links

David A. Corneth, Table of n, a(n) for n = 1..12224 (Using Luhn table from A022006)

Example

1 is in the sequence as 100*1 + 1 = 101, 100*1 + 3 = 103, 100*1 + 7 = 107, 100*1 + 9 = 109, 100*1 + 13= 113, 100*1 + 27 = 127 are consecutive primes of the form 100k+1, 100k+3, 100k+7, 100k+9, 100k+13, 100k+27 respectively where k = 1. - David A. Corneth, Jun 21 2022

Prog

(PARI) is(n) = {my(v = [100*n+1, 100*n+3, 100*n+7, 100*n+9, 100*n+13, 100*n+27], t = 0); forprime(p = 100*n+1, oo, t++; if(v[t] != p, return(0)); if(t >= 6, return(1)))} \\ David A. Corneth, Jun 21 2022
(Python)
from sympy import nextprime
def ok(n):
    t, targets = 100*n, [100*n+d for d in [1, 3, 7, 9, 13, 27]]
    return all((t:=nextprime(t)) == targets[i] for i in range(6))
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, Jun 21 2022

Crossrefs

Cf. A022006, A031932.

Sequence in context: A250949 A276567 A216291 * A237970 A218399 A090060

Adjacent sequences: A216287 A216288 A216289 * A216291 A216292 A216293

Keyword

nonn

Author

V. Raman, Sep 03 2012

Status

approved