A101730 Indices of primes in sequence defined by A(0) = 43, A(n) = 10*A(n-1) + 33 for n > 0.

0, 1, 2, 3, 5, 6, 7, 11, 22, 58, 74, 143, 203, 267, 759, 1215, 1429, 1505, 1508, 2803, 2923, 3200, 3304, 5752, 9267, 11278, 19676, 23413, 28626, 31361, 42298, 49118, 63746, 81766

Offset: 1

Author

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

Keywords

• nonn
• hard
• more

Comments

Numbers n such that (420*10^n - 33)/9 is prime.

Numbers n such that digit 4 followed by n >= 0 occurrences of digit 6 followed by digit 3 is prime.

Numbers corresponding to terms <= 759 are certified primes.

a(35) > 10^5. - Robert Price, Mar 30 2015

Examples

			463 is prime, hence 1 is a term.
		

References

• Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.

Links

• Makoto Kamada, Prime numbers of the form 466...663.
• Index entries for primes involving repunits.

Crossrefs

Cf. A000533, A002275, A099005.

Programs

Mathematica

Select[Range[0, 100], PrimeQ[(420*10^# - 33)/9] &]

PARI

a=43;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a+33)

PARI

for(n=0,1500,if(isprime((420*10^n-33)/9),print1(n,",")))

Formula

a(n) = A099005(n) - 1.

Extensions

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

a(28)-a(34) derived from A099005 by Robert Price, Mar 30 2015