A101006 Indices of primes in sequence defined by A(0) = 91, A(n) = 10*A(n-1) + 31 for n > 0.

1, 3, 7, 2959, 4570, 5200, 17863, 21921, 89374

Offset

1,2

Comments

Numbers n such that (850*10^n - 31)/9 is prime.

Numbers n such that digit 9 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(10) > 10^5. - Robert Price, Nov 07 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..9.

Makoto Kamada, Prime numbers of the form 944...441.

Index entries for primes involving repunits.

Formula

a(n) = A103097(n) - 1.

Example

944444441 is prime, hence 7 is a term.

Mathematica

Select[Range[0, 100000], PrimeQ[(850*10^# - 31)/9] &] (* Robert Price, Nov 07 2015 *)

Prog

(PARI) a=91; for(n=0, 3000, if(isprime(a), print1(n, ", ")); a=10*a+31)
(PARI) for(n=0, 3000, if(isprime((850*10^n-31)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A103097.

Sequence in context: A175986 A296351 A349007 * A306632 A083461 A137029

Adjacent sequences: A101003 A101004 A101005 * A101007 A101008 A101009

Keyword

nonn,hard,more,less

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Nov 27 2004

Extensions

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

a(7)-a(8) from Kamada data by Ray Chandler, Apr 28 2015

a(9) from Robert Price, Nov 07 2015

Status

approved