A101139 Indices of primes in sequence defined by A(0) = 71, A(n) = 10*A(n-1) + 31 for n > 0.

0, 3, 5, 6, 9, 15, 21, 30, 1314, 2063, 6149, 8706, 12251, 18609, 21629, 41711, 44807, 45420

Offset

1,2

Comments

Numbers n such that (670*10^n - 31)/9 is prime.

Numbers n such that digit 7 followed by n >= 0 occurrences of digit 4 followed by digit 1 is prime.

Some of the larger entries may only correspond to probable primes.

a(19) > 10^5. - Robert Price, Sep 28 2015

References

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

Links

Table of n, a(n) for n=1..18.

Makoto Kamada, Prime numbers of the form 744...441.

Index entries for primes involving repunits.

Formula

a(n) = A103057(n) - 1.

Example

74441 is prime, hence 3 is a term.

Mathematica

Select[Range[0, 100000], PrimeQ[(670*10^# - 31)/9] &] (* Robert Price, Sep 28 2015 *)

Prog

(PARI) a=71; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a+31)
(PARI) for(n=0, 1500, if(isprime((670*10^n-31)/9), print1(n, ", ")))
(Magma) [n: n in [0..1000] | IsPrime((670*10^n-31) div 9)]; // Vincenzo Librandi, Sep 29 2015

Crossrefs

Cf. A000533, A002275, A103057.

Sequence in context: A070111 A070117 A176345 * A309140 A102606 A102372

Adjacent sequences: A101136 A101137 A101138 * A101140 A101141 A101142

Keyword

nonn,hard,more

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 03 2004

Extensions

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

a(13)-a(18) from Kamada data by Ray Chandler, Apr 30 2015

Status

approved