A101826 Indices of primes in sequence defined by A(0) = 37, A(n) = 10*A(n-1) - 53 for n > 0.

0, 1, 217, 691, 1804, 2206, 2872, 59134

Offset

1,3

Comments

Numbers n such that (280*10^n + 53)/9 is prime.

Numbers n such that digit 3 followed by n >= 0 occurrences of digit 1 followed by digit 7 is prime.

Numbers corresponding to terms <= 691 are certified primes.

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..8.

Makoto Kamada, Prime numbers of the form 311...117.

Index entries for primes involving repunits.

Formula

a(n) = A101393(n) - 1.

Example

317 is prime, hence 1 is a term.

Mathematica

nn=2900; Transpose[Select[Thread[{NestList[10#-53&, 37, nn], Range[0, nn]}], PrimeQ[First[#]]&]] [[2]] (* Harvey P. Dale, Mar 26 2011 *)

Prog

(PARI) a=37; for(n=0, 2000, if(isprime(a), print1(n, ", ")); a=10*a-53)
(PARI) for(n=0, 2000, if(isprime((280*10^n+53)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A101393.

Sequence in context: A020232 A019422 A231558 * A262052 A020251 A320715

Adjacent sequences: A101823 A101824 A101825 * A101827 A101828 A101829

Keyword

nonn,hard,more

Author

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

Extensions

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

a(8) derived from A101393 by Robert Price, Jan 26 2015

Status

approved