A100998 Indices of primes in sequence defined by A(0) = 97, A(n) = 10*A(n-1) - 63 for n > 0.

0, 1, 2, 3, 4, 14, 18, 19, 45, 51, 52, 191, 379, 587, 775, 905, 1349, 1735, 2913, 7507, 15709, 16452, 17487, 18108, 21603, 25890, 26724, 34837, 67467

Offset: 1

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Nov 27 2004

Keywords

• nonn
• hard
• more

Comments

Numbers n such that 90*10^n + 7 is prime.

Numbers n such that digit 9 followed by n >= 0 occurrences of digit 0 followed by digit 7 is prime.

Numbers corresponding to terms <= 1349 are certified primes.

a(30) > 2*10^5. - Robert Price, Oct 16 2015

Examples

			90007 is prime, hence 3 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 900...007.
• Index entries for primes involving repunits.

Crossrefs

Cf. A000533, A002275, A096774.

Programs

Mathematica

Select[Range[0, 200000], PrimeQ[90*10^# + 7] &] (* Robert Price, Oct 16 2015 *)

PARI

a=97;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-63)

PARI

for(n=0,1500,if(isprime(90*10^n+7),print1(n,",")))

Formula

a(n) = A096774(n) - 1.

Extensions

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

a(25)-a(29) from Kamada data by Ray Chandler, Apr 28 2015