1,2

For an arithmetical function f, call the arguments n such that f(reverse(n)) = reverse(f(n)) the "palinpoints" of f. This sequence is the sequence of palinpoints of f(n) = sigma(n).

If n is in the sequence and 10 doesn't divide n then the reversal of n is also in the sequence. - Farideh Firoozbakht (f.firoozbakht(AT)sci.ui.ac.ir), Aug 31 2004

Comments from Farideh Firoozbakht (mymontain(AT)yahoo.com), Jan 16 2005. "The largest term that I found is M=(58*100^687 - 157)/33; the length of M is 1375. I proved the following facts about this sequence:

"I : If p=(58*100^n - 157)/99 is prime then 3*p is in the sequence, the sequence A102285 gives such n's.

"II : If p=(59*100^n - 257)/99 is prime then 3*p is in the sequence, I found only two primes of this form the first for n=3 and the second for n=27, next such n is greater than 3400.

"III : If both numbers p=10^n - 3 & q=5*10^n - 9 are primes then both numbers 2*p & q are in the sequence, q is reversal of 2*p. I found only two such n's, n=1 & 2.

"IV : If both numbers p=(10^n-7)/3 & q=(127*10^(n-1)-7)/3 are primes then both numbers 4*p & q are in the sequence, q is the reversal of 4*p, the sequence A102287 are these terms of A069514, I found only four such n's, n=2,3,4 & 6."

Let f(n) = sigma(n). Then f(194) = 294, f(491) = 492, so f(reverse(194)) = reverse(f(194)). Therefore 194 belongs to the sequence.

rev[n_] := FromDigits[Reverse[IntegerDigits[n]]]; f[n_] := DivisorSigma[1, n]; Select[Range[10^6], f[rev[ # ]] == rev[f[ # ]] &]

Cf. A102285, A102286, A102287.

Sequence in context: A048331 A133476 A131023 this_sequence A101012 A048659 A065774

Adjacent sequences: A069511 A069512 A069513 this_sequence A069515 A069516 A069517

base,nonn

Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Apr 15 2002

More terms from Farideh Firoozbakht (f.firoozbakht(AT)sci.ui.ac.ir), Aug 31 2004