cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A099190 Numbers n such that 8*10^n-7 is prime.

Original entry on oeis.org

1, 3, 5, 6, 10, 12, 13, 39, 48, 54, 64, 82, 147, 148, 360, 399, 1638, 1876, 2146, 2194, 15789, 23074, 38466, 68400
Offset: 1

Views

Author

Robert G. Wilson v, Oct 01 2004

Keywords

Comments

Also numbers n such that 7*10^n + 9*R_n - 6 is prime, where R_n = 11...1 is the repunit (A002275) of length n.
Primes of the form 7*10^n+9R_n-6 are the only primes which are one more than twice their reversal.
a(25) > 2*10^5. - Robert Price, Nov 11 2015

Examples

			73, 7993, 799993, 7999993, etc. are primes.
		

Crossrefs

Programs

  • Mathematica
    Do[ If[ PrimeQ[8*10^n - 7], Print[n]], {n, 10000}]
  • PARI
    is(n)=ispseudoprime(8*10^n-7) \\ Charles R Greathouse IV, Feb 20 2017

Formula

a(n) = A101155(n) + 1.

Extensions

a(19) & a(20) from Robert G. Wilson v, Jan 19 2005
a(21)-a(24) from Kamada data by Robert Price, Dec 14 2010

A169830 Numbers k such that 2*reverse(k) - k = 1.

Original entry on oeis.org

1, 73, 793, 7993, 79993, 799993, 7999993, 79999993, 799999993, 7999999993, 79999999993, 799999999993, 7999999999993, 79999999999993, 799999999999993, 7999999999999993, 79999999999999993, 799999999999999993, 7999999999999999993, 79999999999999999993, 799999999999999999993
Offset: 1

Views

Author

N. J. A. Sloane, May 31 2010

Keywords

Comments

The sequence is infinite since it contains all numbers of the form 799...9993. (Cf. A101155, A101849.) [Ulrich Krug (leuchtfeuer37(AT)gmx.de), Jun 02 2010]
All numbers of the form 8*10^k-7 are members, but are there any others? - Robert G. Wilson v, Jun 01 2010
All solutions are of the form 8*10^k-7. - David Radcliffe, Jul 25 2015

Crossrefs

Same sequence as A100412.
Digit reversals of A083818.

Programs

  • Mathematica
    k = 1; lst = {}; fQ[n_] := 2 FromDigits@ Reverse@ IntegerDigits@n == 1 + n; While[k < 10^8, If[fQ@k, Print@k; AppendTo[lst, k]]; k++ ]; lst (* Robert G. Wilson v, Jun 01 2010 *)
    Rest@ CoefficientList[Series[x (1 + 62 x)/((1 - x) (1 - 10 x)), {x, 0, 20}], x] (* or *)
    Table[If[n == 1, 1, FromDigits@ Join[{7}, ConstantArray[9, n - 2], {3}]], {n, 20}] (* or *)
    LinearRecurrence[{11, -10}, {1, 73}, 20] (* Michael De Vlieger, Feb 12 2017 *)
  • PARI
    isok(n) = 2*fromdigits(Vecrev(digits(n))) - n == 1; \\ Michel Marcus, Feb 12 2017

Formula

a(n) = 8*10^(n-1) - 7. - David Radcliffe, Jul 25 2015
From Matthew House, Feb 12 2017: (Start)
G.f.: x*(1+62*x)/((1-x)*(1-10*x)).
a(n) = 11*a(n-1) - 10*a(n-2). (End)
E.g.f.: (31 - 35*exp(x) + 4*exp(10*x))/5. - Elmo R. Oliveira, Jun 12 2025

Extensions

a(6)-a(8) from Robert G. Wilson v, Jun 01 2010
More terms from David Radcliffe, Jul 25 2015

A101849 Indices of primes in sequence defined by A(0) = 37, A(n) = 10*A(n-1) + 27 for n > 0.

Original entry on oeis.org

0, 1, 13, 19, 29, 43, 65, 259, 871, 8845, 26743, 57505, 98471, 106891
Offset: 1

Views

Author

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

Keywords

Comments

Numbers n such that (360*10^n - 27)/9 is prime.
Numbers n such that digit 3 followed by n >= 0 occurrences of digit 9 followed by digit 7 is prime.
Numbers corresponding to terms <= 871 are certified primes.
a(14) > 10^5. - Robert Price, Mar 17 2015.
a(15) > 2*10^5. - Robert Price, Oct 02 2015

Examples

			397 is prime, hence 1 is a term.
		

References

  • Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.

Crossrefs

Programs

  • Mathematica
    Select[Range[0, 1000], PrimeQ[(360*10^# - 27)/9] &] (* Robert Price, Mar 17 2015 *)
  • PARI
    a=37;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a+27)
    
  • PARI
    for(n=0,1500,if(isprime((360*10^n-27)/9),print1(n,",")))

Formula

a(n) = A101398(n) - 1.

Extensions

8845 from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008
a(11)-a(13) derived from A101398 by Robert Price, Mar 17 2015
a(14) from Robert Price, Oct 02 2015
Showing 1-3 of 3 results.