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A102007

Indices of primes in sequence defined by A(0) = 17, A(n) = 10*A(n-1) - 63 for n > 0.

0, 1, 3, 7, 8, 23, 59, 109, 133, 221, 411, 699, 998, 1382, 5075, 5542, 6343, 14599, 15092, 21716, 23635, 30220, 50710, 221627, 350070, 371695, 487290, 995255, 1043371

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OFFSET

1,3

COMMENTS

Numbers k such that 10*10^k + 7 is prime.

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

Numbers corresponding to terms <= 998 are certified primes.

a(24) > 2*10^5. - Robert Price, Nov 09 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..29.

Makoto Kamada, Prime numbers of the form 100...007.

FORMULA

a(n) = A088274(n) - 1.

EXAMPLE

10007 is prime, hence 3 is a term.

MATHEMATICA

Select[Range[0, 100000], PrimeQ[10*10^# + 7] &] (* Robert Price, Nov 09 2015 *)

PROG

(PARI) a=17; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a-63)

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

CROSSREFS

Cf. A000533, A002275, A088274.

Sequence in context: A369920 A244532 A037208 * A152486 A301523 A105756

Adjacent sequences: A102004 A102005 A102006 * A102008 A102009 A102010

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(24)-a(28) added from A088274 by Amiram Eldar, Nov 28 2021

a(29) derived from A088274 by Elmo R. Oliveira, Dec 15 2025

STATUS

approved

URL: https://oeis.org/A102007

⇱ A102007 - OEIS