A102006 Indices of primes in sequence defined by A(0) = 13, A(n) = 10*A(n-1) - 27 for n > 0.

0, 1, 4, 5, 10, 16, 17, 38, 55, 100, 104, 106, 122, 412, 425, 2606, 7667, 10469, 11020, 17752, 26926, 60775, 98287, 300475

Offset

1,3

Comments

Numbers n such that 10*10^n + 3 is prime.

Numbers n such that digit 1 followed by n >= 0 occurrences of digit 0 followed by digit 3 is prime.

Numbers corresponding to terms <= 425 are certified primes.

No other terms <99,999.

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 100...003.

Formula

a(n) = A049054(n) - 1.

Example

100003 is prime, hence 4 is a term.

Prog

(PARI) a=13; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a-27)
(PARI) for(n=0, 1500, if(isprime(10*10^n+3), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A049054, A159352.

Sequence in context: A135104 A131780 A354968 * A118735 A002970 A073611

Adjacent sequences: A102003 A102004 A102005 * A102007 A102008 A102009

Keyword

nonn,hard,more

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 28 2004

Extensions

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

a(22)=60775, a(23)=98287 from Robert Price, Mar 03 2011

a(24) from A049054 by Ray Chandler, May 01 2015

Status

approved