A101726 Indices of primes in sequence defined by A(0) = 43, A(n) = 10*A(n-1) + 23 for n > 0.

0, 3, 6, 18, 33, 53, 77, 89, 212, 306, 701, 1455, 2138, 2213, 3065, 9299, 16439, 16893, 28574, 54050

Offset

1,2

Comments

Numbers n such that (410*10^n - 23)/9 is prime.

Numbers n such that digit 4 followed by n >= 0 occurrences of digit 5 followed by digit 3 is prime.

Numbers corresponding to terms <= 701 are certified primes.

a(21) > 10^5. Robert Price, May 08 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..20.

Makoto Kamada, Prime numbers of the form 455...553.

Index entries for primes involving repunits.

Formula

a(n) = A102991(n+1) - 1.

Example

45553 is prime, hence 3 is a term.

Mathematica

Select[Range[0, 300], PrimeQ[(410*10^# - 23)/9] &] (* Robert Price, May 08 2015 *)

Prog

(PARI) a=43; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a+23)
(PARI) for(n=0, 1500, if(isprime((410*10^n-23)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A102991.

Sequence in context: A277317 A277318 A277316 * A034457 A268529 A026532

Adjacent sequences: A101723 A101724 A101725 * A101727 A101728 A101729

Keyword

nonn,hard,more

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 14 2004

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

a(17)-a(19) from Kamada data by Ray Chandler, Apr 30 2015

a(20) from Robert Price, May 08 2015

Status

approved