A101144 Indices of primes in sequence defined by A(0) = 73, A(n) = 10*A(n-1) + 23 for n > 0.

0, 3, 17, 18, 645, 813, 5793, 16523, 19494, 26009, 29237, 72119

Offset

1,2

Comments

Numbers n such that (680*10^n - 23)/9 is prime.

Numbers n such that digit 7 followed by n >= 0 occurrences of digit 5 followed by digit 3 is prime.

Numbers corresponding to terms <= 813 are certified primes.

a(13) > 10^5. - Robert Price, Oct 01 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..12.

Makoto Kamada, Prime numbers of the form 755...553.

Index entries for primes involving repunits.

Formula

a(n) = A103061(n+1) - 1.

Example

75553 is prime, hence 3 is a term.

Mathematica

nn=5800; Transpose[Select[Thread[{NestList[10#+23&, 73, nn], Range[0, nn]}], PrimeQ[First[#]]&]][[2]] (* Harvey P. Dale, May 02 2011 *)
Select[Range[0, 100000], PrimeQ[(680*10^# - 23)/9] &] (* Robert Price, Oct 01 2015 *)

Prog

(PARI) a=73; for(n=0, 1000, if(isprime(a), print1(n, ", ")); a=10*a+23)
(PARI) for(n=0, 1000, if(isprime((680*10^n-23)/9), print1(n, ", ")))
(Magma) [n: n in [0..100]| IsPrime((680*10^n-23) div 9)]; // Vincenzo Librandi, Oct 02 2015

Crossrefs

Cf. A000533, A002275, A103061.

Sequence in context: A293764 A295395 A246143 * A038886 A019342 A340408

Adjacent sequences: A101141 A101142 A101143 * A101145 A101146 A101147

Keyword

nonn,hard,more

Author

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

Extensions

5793 from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

a(8)-a(11) from Kamada data by Ray Chandler, Apr 30 2015

a(12) from Robert Price, Oct 01 2015

Status

approved