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

Author

V. Raman, Sep 03 2012

Keywords

• nonn

Examples

			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
		

Links

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

Crossrefs

Cf. A022006, A031932.

Programs

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