A227432 -id:A227432 - cp's OEIS frontend

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

Abhiram R Devesh, Aug 02 2014

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

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

Cf. A023200, A152052, A227432, A240170.

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

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)

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

A227435 Difference between 10^n and the first prime of gap 6 > 10^n.

Original entry on oeis.org

13, 31, 13, 61, 43, 187, 223, 217, 87, 97, 57, 163, 267, 133, 273, 2473, 13, 3, 91, 757, 367, 421, 531, 177, 343, 673, 1753, 721, 847, 6331, 1081, 1141, 6583, 2191, 957, 1563, 423, 3951, 81, 8497, 1477, 7723, 11311, 12691, 5817, 8751, 2251, 4761, 12627, 1521, 1281, 11283, 11577, 3201, 3991, 3

Offset: 1

Pierre CAMI, Jul 11 2013

nonn

As N increases, the ratio sum(a(n)/n^2)/N for n = 1 to N tends to 2.

			10^1+13 = 23, 23 and 29 primes of gap 6 so a(1)=13.

Pierre CAMI, Table of n, a(n) for n = 1..272

Cf. A124001, A227432.

cp's OEIS Frontend

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

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