A102284 -id:A102284 - cp's OEIS frontend

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

275, 295, 2995, 299995, 2999995, 278736495, 299999995, 299999999995

Offset: 1

Joseph L. Pe, May 12 2002

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

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

Cf. A056716, A102284.

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

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

A102280 Let k = n-th number == 1 or 5 mod 6 (A007310(n)); consider the generalized 3x+1 map T_k defined by T_k(n) = (3n+k)/2 if n odd, n/2 if n even; then a(n) = smallest positive number m which is in a primitive cycle of T_k.

Original entry on oeis.org

1, 1, 5, 1, 1, 1, 5, 5, 7, 1, 13, 13, 19, 1, 1, 5, 25, 103, 1, 1, 1, 19, 17, 29, 5, 1, 1, 65, 7, 17, 1, 1, 1, 7, 5, 1, 19, 1, 13, 1, 5, 1, 1, 13, 11, 1, 11, 7, 1, 19, 41, 1, 13, 11, 11, 13, 11, 7, 29, 5, 11, 1, 5, 47, 1, 5, 13, 1, 43, 1, 37, 1, 17, 5, 35, 5, 7, 5, 11, 1, 7, 43, 1, 91, 1, 1, 29, 7, 47, 55, 17, 1, 13

Offset: 1

N. J. A. Sloane, Feb 19 2005

nonn

Geoffrey H. Morley, Table of n, a(n) for n = 1..10000
J. C. Lagarias, The set of rational cycles for the 3x+1 problem, Acta Arith. 56 (1990), 33-53. - See Table 3.1 on page 41.

Cf. A102284, A007310, A226633.

a(12)[k=35] and a(25)[k=73] corrected and more terms added by Geoffrey H. Morley, Mar 14 2013

A226634 Length of the primitive 3x-k cycle associated with A226633(n).

Original entry on oeis.org

1, 4, 6, 17, 19, 34, 12, 9, 5, 22, 12, 17, 17, 69, 7, 18, 44, 38, 22, 48, 6, 68, 44, 30, 54, 38, 68, 14, 22, 44, 23, 30, 84, 8, 17, 17, 30, 12, 68, 18, 7, 66, 30, 22, 85, 10, 14, 66, 44, 30, 14, 54, 44, 12, 68, 44, 9, 38, 34, 14, 55, 8, 56, 50, 36, 44, 25, 37

Offset: 1

Geoffrey H. Morley, Jun 14 2013

nonn

Geoffrey H. Morley, Table of n, a(n) for n = 1..600

Cf. A102284.

cp's OEIS Frontend

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

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A102280 Let k = n-th number == 1 or 5 mod 6 (A007310(n)); consider the generalized 3x+1 map T_k defined by T_k(n) = (3n+k)/2 if n odd, n/2 if n even; then a(n) = smallest positive number m which is in a primitive cycle of T_k.

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A226634 Length of the primitive 3x-k cycle associated with A226633(n).

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