A230007 Numbers n such that sigma(n) = reversal(n+7).

62, 206, 6002, 6439562, 60000002, 6004356002, 29355232298, 60000000002, 292369967108, 600439956002, 643956439562, 6303723993362

Offset

1,1

Comments

If p=3*10^m+1 is prime then 2*p is in the sequence.

Also if p=322*10^m-219 is prime then 2*p is in the sequence. 206, 6002 and 6439562 are of this form. It is interesting that 6002 = 2*(3*10^3+1) = 2*(322*10^1-219) is of both two forms.

Let f(r,s,t) = 3*10^(t*(s+4)+2*r+1)+10^(r+1)*(22*(10^(s+2)-1)*(10^(t*(s+4))-1)/ (10^(s+4)-1))+1, if p=f(r,s,t) is prime and (i) r, s and t are nonnegative integers or (ii) s=t=0 and 2r is a positive integer or (iii) r=t=0 and s=-3, then 2*p is in the sequence. Note, very interestingly, this pattern is a generalization of the previous two forms mentioned above. In fact we have 3*10^(m+1)+1 = f(m/2,s,0) and 322*10^m-219 = f(0,m-3,1). - Farideh Firoozbakht, Dec 17 2013

Links

Table of n, a(n) for n=1..12.

Formula

a(1)=2*f(0,s,0), a(2)=2*f(0,-3,1), a(3)=2*f(1,s,0), a(4)=2*f(0,1,1), a(5)=2*f(3,s,0), a(6)=2*f(2,0,1), a(8)=2*f(9/2,s,0), a(10)=2*f(2,2,1), a(11)=2*f(0,1,2), where f(r,s,t) = 3*10^(t*(s+4)+2*r+1) +10^(r+1)*(22*(10^(s+2)-1)*(10^(t*(s+4))-1) / (10^(s+4)-1))+1.

Example

sigma(206) = 312 = reversal(213) = reversal(206+7).

Mathematica

Do[If[c=FromDigits[Reverse[IntegerDigits[7+n]]]; c>n && DivisorSigma[1, n] == c, Print[n]], {n, 500000000}]

Crossrefs

Cf. A000203, A004086, A230009, A230021.

Sequence in context: A045274 A045175 A100423 * A318561 A234490 A234483

Adjacent sequences: A230004 A230005 A230006 * A230008 A230009 A230010

Keyword

nonn,base,more

Author

Farideh Firoozbakht, Dec 12 2013

Extensions

a(6)-a(12) from Giovanni Resta, Dec 13 2013

Status

approved