A101525 Indices of primes in sequence defined by A(0) = 61, A(n) = 10*A(n-1) + 21 for n > 0.

0, 1, 3, 6, 17, 18, 22, 23, 33, 40, 55, 63, 83, 148, 271, 754, 1271, 2397, 2685, 4799, 5197, 6216, 8736, 12387, 12390, 19701, 42403

Offset: 1

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 06 2004

Keywords

• nonn
• hard
• more

Comments

Numbers n such that (570*10^n - 21)/9 is prime.

Numbers n such that digit 6 followed by n >= 0 occurrences of digit 3 followed by digit 1 is prime.

Numbers corresponding to terms <= 754 are certified primes.

a(28) > 10^5. - Robert Price, Sep 10 2015

Examples

			631 is prime, hence 1 is a term.
		

References

• Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.

Links

• Makoto Kamada, Prime numbers of the form 633...331.
• Index entries for primes involving repunits.

Crossrefs

Cf. A000533, A002275, A103032.

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[(570*10^# - 21)/9] &] (* Robert Price, Sep 10 2015 *)

PARI

a=61;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a+21)

PARI

for(n=0,1500,if(isprime((570*10^n-21)/9),print1(n,",")))

Formula

a(n) = A103032(n) - 1.

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

a(24)-a(27) from Kamada data by Ray Chandler, Apr 30 2015