cp's OEIS Frontend

A069514 Numbers n such that sigma(reversal(n)) = reversal(sigma(n)). Ignore leading 0's.

%I A069514 #9 Feb 11 2014 19:05:28
%S A069514 1,2,3,4,5,7,14,41,124,194,333,421,491,1324,4231,13324,17054,17571,
%T A069514 42331,45071,120530,138465,386650,564831,1130324,1216360,1333324,
%U A069514 1727571,1757271,1757571,1787871,2249422,4230311,4233331,4369634
%N A069514 Numbers n such that sigma(reversal(n)) = reversal(sigma(n)). Ignore leading 0's.
%C A069514 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).
%C A069514 If n is in the sequence and 10 doesn't divide n then the reversal of n is also in the sequence. - _Farideh Firoozbakht_, Aug 31 2004
%C A069514 Comments from _Farideh Firoozbakht_, 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:
%C A069514 "I : If p=(58*100^n - 157)/99 is prime then 3*p is in the sequence, the sequence A102285 gives such n's.
%C A069514 "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.
%C A069514 "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.
%C A069514 "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."
%e A069514 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.
%t A069514 rev[n_] := FromDigits[Reverse[IntegerDigits[n]]]; f[n_] := DivisorSigma[1, n]; Select[Range[10^6], f[rev[ # ]] == rev[f[ # ]] &]
%Y A069514 Cf. A102285, A102286, A102287.
%K A069514 base,nonn
%O A069514 1,2
%A A069514 _Joseph L. Pe_, Apr 15 2002
%E A069514 More terms from _Farideh Firoozbakht_, Aug 31 2004