A101009 Indices of primes in sequence defined by A(0) = 91, A(n) = 10*A(n-1) + 41 for n > 0.

2, 5, 17, 29, 87, 92, 153, 176, 227, 572, 896, 980, 1415, 1449, 3365, 4931, 5193, 13478, 18608, 23345, 51423, 74675, 80570

Offset

1,1

Comments

Numbers n such that (860*10^n - 41)/9 is prime.

Numbers n such that digit 9 followed by n >= 0 occurrences of digit 5 followed by digit 1 is prime.

Numbers corresponding to terms <= 980 are certified primes.

a(24) > 10^5. - Robert Price, Nov 10 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..23.

Makoto Kamada, Prime numbers of the form 955...551.

Index entries for primes involving repunits.

Formula

a(n) = A103100(n+1) - 1.

Example

9551 is prime, hence 2 is a term.

Mathematica

Flatten[Position[NestList[10#+41&, 91, 5200], _?PrimeQ]-1] (* Harvey P. Dale, Jun 28 2012 *)
Select[Range[0, 100000], PrimeQ[(860*10^# - 41)/9] &] (* Robert Price, Nov 10 2015 *)

Prog

(PARI) a=91; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a+41)
(PARI) for(n=0, 1500, if(isprime((860*10^n-41)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A103100.

Sequence in context: A019353 A106882 A172122 * A269018 A066649 A075345

Adjacent sequences: A101006 A101007 A101008 * A101010 A101011 A101012

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(18)-a(20) from Kamada data by Ray Chandler, Apr 28 2015

a(21)-a(23) from Robert Price, Nov 10 2015

Status

approved