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.

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.

Crossrefs

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

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

A083818 Numbers k such that 2k-1 is the digit reversal of k.

Original entry on oeis.org

1, 37, 397, 3997, 39997, 399997, 3999997, 39999997, 399999997, 3999999997, 39999999997, 399999999997, 3999999999997, 39999999999997, 399999999999997, 3999999999999997, 39999999999999997, 399999999999999997, 3999999999999999997, 39999999999999999997, 399999999999999999997
Offset: 1

Views

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 08 2003

Keywords

Comments

a(n) = 1 + 36 + 360 + 3600 + 36000 + ..., for a total of n terms. a(n) = 1 + sum of first n-1 terms of the geometric progression with first term 36 and common ratio 10. a(n) = 1 + 36*A000042(n-1) (the unary sequence).

Examples

			2*37 - 1 = 73.
		

Crossrefs

Digit reversals of A169830.

Programs

  • PARI
    my(x='x+O('x^22)); Vec(x*(1+26*x)/((1-x)*(1-10*x))) \\ Elmo R. Oliveira, Jun 12 2025

Formula

a(n) = 4*10^(n-1) - 3.
From Elmo R. Oliveira, Jun 12 2025: (Start)
G.f.: x*(26*x+1)/((x-1)*(10*x-1)).
E.g.f.: (13 - 15*exp(x) + 2*exp(10*x))/5.
a(n) = 11*a(n-1) - 10*a(n-2) for n >= 3. (End)

Extensions

a(1)=1 inserted by David Radcliffe, Jul 25 2015
Showing 1-3 of 3 results.