A114926 -id:A114926 - cp's OEIS frontend

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

Joseph L. Pe, Jul 21 2002

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

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

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

Cf. A114926, A114927.

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

More terms from Farideh Firoozbakht, Jan 27 2006

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

A100415 Numbers n such that n is R(n)-th nonprime number, where R(n) is the digit reversal of n (A018252(A004086(n))=n).

Original entry on oeis.org

1, 64, 524, 534, 58725, 907538, 6264385, 9438088, 9596598, 27895162, 422984004, 548911025, 8804661048, 49640253574, 63899981216, 95138721219, 97895906839, 469449672154

Offset: 1

Farideh Firoozbakht, Dec 12 2004

n is in the sequence iff n is not prime and R(n)=n-pi(n). There is no further term up to 3670000000.

a(19) > 10^13. Up to that limit, this sequence contains all the numbers k such that R(k) = k - pi(k). - Giovanni Resta, Aug 08 2019

			548911025 is in the sequence because 548911025 is the 520118945th nonprime natural number.

Cf. A018252, A004086, A100413, A100414, A114926.

Do[s = FromDigits[Reverse[IntegerDigits[n]]]; If[ ! PrimeQ[n] && s == n - PrimePi[n], Print[n]], {n, 548911025}]

a(13)-a(18) from Giovanni Resta, Aug 08 2019

cp's OEIS Frontend

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

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