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.

A070272 Numbers n such that reverse(n) = phi(n) + sigma(n).

Original entry on oeis.org

275, 295, 2995, 299995, 2999995, 278736495, 299999995, 299999999995
Offset: 1

Views

Author

Joseph L. Pe, May 12 2002

Keywords

Comments

For n>0 5*(6*10^A056716(n)-1) is in this sequence. In fact if p = 6*10^n-1 is prime and n>0 (p>5) then m = 5*p is in the sequence. That's because phi(m) = phi(5*p) = 4*(6*10^n-2) = 24*10^n-8 and sigma(m)= 6*6*10^n, so phi(m) + sigma(m) = 6*10^(n+1)-8 = 5.(9)(n).2 = reversal(2.(9)(n).5) = reversal (3*10^(n+1)-5) = reversal(m)(dot between numbers means concatenation and "(9)(n)" means number of 9's is n). For example 299999995 is in the sequence because 6*10^7-1 is prime and 299999995 = 5*(6*10^7-1); 299999999995 is in sequence because 6*10^10-1 is prime and 299999999995 = 5*(6*10^10-1). Next term is greater than 80000000. - Farideh Firoozbakht, Jan 11 2005
Next term is greater than 10^9. - Farideh Firoozbakht, Jan 23 2005
a(9) > 10^13. - Giovanni Resta, Feb 08 2014

Examples

			Reverse(275) = 572 = 200 + 372 = phi(275) + sigma(275).
		

Crossrefs

Programs

  • Mathematica
    Select[Range[10^6], FromDigits[Reverse[IntegerDigits[ # ]]] == EulerPhi[ # ] + DivisorSigma[1, # ] &]

Extensions

One more term from Farideh Firoozbakht, Jan 11 2005
More terms from Farideh Firoozbakht, Jan 23 2005
a(8) from Giovanni Resta, Nov 03 2012