A072393 Numbers n such that n - reverse(n) = phi(n).

91, 874, 3411, 9093, 40112, 44252, 54081, 67284, 80224, 90933, 91503, 4961782, 5400081, 5726691, 8750834, 9076921, 9155055, 54000081, 62023914, 90766921, 93079231, 430770922, 540000081, 636355044, 808618664, 907666921, 928709013, 4050394312, 4262971312

Offset: 1

Author

Joseph L. Pe, Jul 21 2002

Keywords

• base
• nonn

Comments

If m>1 and p=2*10^m+3 is prime then n=27*p is in the sequence because n-reversal(n)=27*(2*10^m+3)-reversal(27*(2*10^m+3))= (54*10^m+81)-(18*10^m+45)=36*10^m+36=18*(2*10^m+2)=phi(27)* phi(2*10^m+3)=phi(27*(2*10^m+3))=phi(n). Also if m>2 and p=(389*10^m+109)/3 is prime then 7*p is in the sequence (the proof is easy). Next term is greater than 2*10^8. - Farideh Firoozbakht, Jan 27 2006

a(51) > 10^12. - Giovanni Resta, Oct 28 2012

Examples

			91 - 19 = 72 = phi(91), so 91 is a term of the sequence.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..50

Crossrefs

Cf. A114926, A114927.

Programs

Mathematica

Select[Range[10^5], # - FromDigits[Reverse[IntegerDigits[n]]] == EulerPhi[ # ] &]

Extensions

More terms from Farideh Firoozbakht, Jan 27 2006

a(22)-a(29) from Donovan Johnson, Dec 04 2011