A240167 Lesser of the first cousin prime pair with n digits.

3, 13, 103, 1009, 10099, 100189, 1000033, 10000453, 100000123, 1000000093, 10000000597, 100000000069, 1000000000189, 10000000000279, 100000000001173, 1000000000000399, 10000000000001719, 100000000000002733, 1000000000000002493, 10000000000000000087

Offset: 1

Author

Abhiram R Devesh, Aug 02 2014

Keywords

• nonn
• base

Comments

Sum of reciprocals converges towards 0.421066...

It is only a (plausible) conjecture that this sequence is well-defined. See A152052. - N. J. A. Sloane, Aug 22 2014

Links

• Abhiram R Devesh, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A023200, A152052, A227432, A240170.

Programs

PARI

a(n)=my(p=nextprime(10^(n-1))); while(!isprime(p+4), p=nextprime(p+1)); return(p)
vector(50, n, a(n)) \\ Derek Orr, Aug 04 2014

Python

import sympy
for i in range(100):
    a=(10**i)
    p=sympy.nextprime(a)
    while not sympy.isprime(p+4):
        p=sympy.nextprime(p)
    print(p)

Formula

For n > 1, a(n) = 10^(n-1) + A227432(n-1), assuming a(n) exists. - Jens Kruse Andersen, Aug 22 2014