A101838 Indices of primes in sequence defined by A(0) = 39, A(n) = 10*A(n-1) - 31 for n > 0.

1, 2, 4, 7, 13, 76, 194, 217, 956, 1051, 1162, 1484, 1730, 1969, 3236, 17353, 85963

Offset

1,2

Comments

Numbers n such that (320*10^n + 31)/9 is prime.

Numbers n such that digit 3 followed by n >= 0 occurrences of digit 5 followed by digit 9 is prime.

Numbers corresponding to terms <= 956 are certified primes.

a(18) > 10^5. - Robert Price, May 31 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..17.

Makoto Kamada, Prime numbers of the form 355...559.

Index entries for primes involving repunits.

Formula

a(n) = A102973(n+1) - 1.

Example

3559 is prime, hence 2 is a term.

Mathematica

For [n = 1, n <= 3000, n++, If[PrimeQ[(320*10^n + 31)/9], Print[n]]] (Steinerberger)

Prog

(PARI) a=39; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a-31)
(PARI) for(n=0, 1500, if(isprime((320*10^n+31)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A102973.

Sequence in context: A102116 A102117 A220124 * A286371 A030135 A222306

Adjacent sequences: A101835 A101836 A101837 * A101839 A101840 A101841

Keyword

nonn,hard

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 20 2004

Extensions

a(9) and a(10) Stefan Steinerberger, Feb 03 2006

3236 from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

a(16) from Kamada data by Ray Chandler, May 01 2015

a(17) from Robert Price, May 31 2015

Status

approved