A101532 Indices of primes in sequence defined by A(0) = 63, A(n) = 10*A(n-1) + 23 for n > 0.

1, 2, 8, 10, 11, 14, 35, 37, 40, 76, 89, 95, 131, 373, 398, 616, 1331, 1394, 1810, 2803, 4952, 5309, 16675, 29335

Offset

1,2

Comments

Numbers n such that (590*10^n - 23)/9 is prime.

Numbers n such that digit 6 followed by n >= 0 occurrences of digit 5 followed by digit 3 is prime.

Numbers corresponding to terms <= 616 are certified primes.

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..24.

Makoto Kamada, Prime numbers of the form 655...553.

Index entries for primes involving repunits.

Formula

a(n) = A103039(n) - 1.

Example

6553 is prime, hence 2 is a term.

Mathematica

Flatten[Position[NestList[10#+23&, 63, 1900], _?PrimeQ]]-1 (* To generate more terms, change the constant 1900 to a larger number, but computation times will increase rapidly. *) (* Harvey P. Dale, May 06 2013 *)

Prog

(PARI) a=63; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a+23)
(PARI) for(n=0, 1500, if(isprime((590*10^n-23)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A103039.

Sequence in context: A088155 A005876 A139370 * A032708 A282094 A084124

Adjacent sequences: A101529 A101530 A101531 * A101533 A101534 A101535

Keyword

nonn,hard,more

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 06 2004

Extensions

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

a(23)-a(24) from Kamada data by Ray Chandler, Apr 30 2015

Status

approved