A077792 -id:A077792

Search: a077792 -id:a077792

Displaying 1-2 of 2 results found.

page 1

A183177

Numbers n such that (10^(2n+1)+15*10^n-1)/3 is prime.

+10
2

1, 7, 85, 94, 273, 356, 1077, 1797, 6758, 30232

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

a(11) > 10^5. - Robert Price, Apr 21 2016

REFERENCES

C. Caldwell and H. Dubner, "Journal of Recreational Mathematics", Volume 28, No. 1, 1996-97, pp. 1-9.

LINKS

Table of n, a(n) for n=1..10.

Patrick De Geest, World!Of Numbers, Palindromic Wing Primes (PWP's)

Makoto Kamada, Prime numbers of the form 33...33833...33

Index entries for primes involving repunits.

FORMULA

a(n) = (A077792(n)-1)/2.

MATHEMATICA

Do[If[PrimeQ[(10^(2n + 1) + 15*10^n - 1)/3], Print[n]], {n, 3000}]

PROG

(PARI) is(n)=ispseudoprime((10^(2*n+1)+15*10^n-1)/3) \\ Charles R Greathouse IV, Jun 13 2017

CROSSREFS

Cf. A004023, A077775-A077798, A107123-A107127, A107648, A107649, A115073, A183174-A183187.

KEYWORD

nonn,more,base

AUTHOR

Ray Chandler, Dec 28 2010

EXTENSIONS

a(10) from Robert Price, Apr 21 2016

STATUS

approved

A332138

a(n) = (10^(2*n+1)-1)/3 + 5*10^n.

+10
2

8, 383, 33833, 3338333, 333383333, 33333833333, 3333338333333, 333333383333333, 33333333833333333, 3333333338333333333, 333333333383333333333, 33333333333833333333333, 3333333333338333333333333, 333333333333383333333333333, 33333333333333833333333333333, 3333333333333338333333333333333

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,1

COMMENTS

See A183177 = {1, 7, 85, 94, 273, 356, ...} for the indices of primes.

LINKS

Table of n, a(n) for n=0..15.

Brady Haran and Simon Pampena, Glitch Primes and Cyclops Numbers, Numberphile video (2015).

Patrick De Geest, Palindromic Wing Primes: (3)8(3), updated: June 25, 2017.

Makoto Kamada, Factorization of 33...33833...33, updated Dec 11 2018.

Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).

FORMULA

a(n) = 3*A138148(n) + 8*10^n = A002277(2n+1) + 5*10^n.

G.f.: (8 - 505*x + 200*x^2)/((1 - x)(1 - 10*x)(1 - 100*x)).

a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.

MAPLE

A332138 := n -> (10^(2*n+1)-1)/3+5*10^n;

MATHEMATICA

Array[ (10^(2 # + 1)-1)/3 + 5*10^# &, 15, 0]

PROG

(PARI) apply( {A332138(n)=10^(n*2+1)\3+5*10^n}, [0..15])

(Python) def A332138(n): return 10**(n*2+1)//3+5*10**n

CROSSREFS

Cf. (A077792-1)/2 = A183177: indices of primes.

Cf. A002275 (repunits R_n = (10^n-1)/9), A002277 (3*R_n), A011557 (10^n).

Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).

Cf. A332118 .. A332178, A181965 (variants with different repeated digit 1, ..., 9).

Cf. A332130 .. A332139 (variants with different middle digit 0, ..., 9).

KEYWORD

nonn,base,easy

AUTHOR

M. F. Hasler, Feb 09 2020

STATUS

approved

page 1

Search completed in 0.006 seconds