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.

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

Links

Crossrefs

Same sequence as A100412.
Digit reversals of A083818.
Cf. A101155, A101849.

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

A101155 Indices of primes in sequence defined by A(0) = 73, A(n) = 10*A(n-1) + 63 for n > 0.

Original entry on oeis.org

0, 2, 4, 5, 9, 11, 12, 38, 47, 53, 63, 81, 146, 147, 359, 398, 1637, 1875, 2145, 2193, 15788, 23073, 38465, 68399
Offset: 1

Views

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 03 2004

Keywords

Comments

Numbers n such that (720*10^n - 63)/9 is prime.
Numbers n such that digit 7 followed by n >= 0 occurrences of digit 9 followed by digit 3 is prime.
Numbers corresponding to terms <= 398 are certified primes.
a(25) > 2*10^5. - Robert Price, Nov 11 2015

Examples

			7999993 is prime, hence 5 is a term.

References

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

Links

Crossrefs

Cf. A000533, A002275, A101849, A169830, A099190.

Programs

  • Mathematica
    Select[Range[0, 100000], PrimeQ[(720*10^# - 63)/9] &] (* Robert Price, Nov 11 2015 *)
  • PARI
    a=73;for(n=0,1000,if(isprime(a),print1(n,","));a=10*a+63)
  • PARI
    for(n=0,1000,if(isprime((720*10^n-63)/9),print1(n,",")))

Formula

a(n) = A099190(n) - 1.

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008
a(21)-a(24) from Kamada data by Ray Chandler, Apr 30 2015

A101398 Numbers k such that 4*10^k-3 is prime.

Original entry on oeis.org

1, 2, 14, 20, 30, 44, 66, 260, 872, 8846, 26744, 57506, 98472, 106892
Offset: 1

Views

Author

Julien Peter Benney (jpbenney(AT)ftml.net), Jan 15 2005

Keywords

Comments

See Kamada link for search limit and prime vs. PRP status.
a(14) > 10^5. - Robert Price, Mar 17 2015
a(15) > 2*10^5. - Robert Price, Oct 02 2015

Examples

			k = 1, 2, 14, 20 are members since 37, 397, 399999999999997 and 399999999999999999997
are prime numbers.

Links

Crossrefs

Cf. A089675, A101849.

Programs

  • Mathematica
    Do[ If[ PrimeQ[4*10^n - 3], Print[n]], {n, 0, 10000}]
  • PARI
    for(n=1, 1e4, if(isprime(4*10^n-3), print1(n", "))) \\ Altug Alkan, Oct 02 2015

Formula

a(n) = A101849(n) + 1.

Extensions

a(11)-a(12) from Kamada data by Robert Price, Dec 13 2010
a(13) from Kamada data by Robert Price, Mar 17 2015
a(14) from Robert Price, Oct 02 2015
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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