A101716 Indices of primes in sequence defined by A(0) = 43, A(n) = 10*A(n-1) - 17 for n > 0.

0, 3, 4, 12, 30, 54, 57, 58, 60, 78, 90, 102, 120, 195, 228, 9438, 13050, 22959, 31296

Offset

1,2

Comments

Numbers n such that (370*10^n + 17)/9 is prime.

Numbers n such that digit 4 followed by n >= 0 occurrences of digit 1 followed by digit 3 is prime.

Numbers corresponding to terms <= 228 are certified primes.

a(20) > 10^5. - Robert Price, May 08 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..19.

Makoto Kamada, Prime numbers of the form 411...113.

Index entries for primes involving repunits.

Formula

a(n) = A102981(n) - 1.

Example

41113 is prime, hence 3 is a term.

Mathematica

Select[Range[0, 300], PrimeQ[(370*10^# + 17)/9] &] (* Robert Price, May 08 2015 *)

Prog

(PARI) a=43; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a-17)
(PARI) for(n=0, 1500, if(isprime((370*10^n+17)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A102981.

Sequence in context: A296271 A000208 A079154 * A360992 A217477 A299809

Adjacent sequences: A101713 A101714 A101715 * A101717 A101718 A101719

Keyword

nonn,hard,more

Author

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

Extensions

9438 from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

a(17)-a(19) from Kamada data by Ray Chandler, Apr 30 2015

Status

approved