A211769 Greater of twin primes p, p+2 with unique values of sigma(p) and sigma(p+2); sigma(n) = A000203(n) = sum of divisors of n.

5, 7, 199, 283, 349, 463, 643, 823, 859, 1291, 1699, 1723, 1789, 1879, 2083, 2143, 2383, 2551, 2803, 3259, 3541, 3559, 3931, 4021, 4243, 4639, 4723, 5443, 5479, 5503, 5659, 6451, 6691, 6703, 6763, 6829, 6949, 7459, 7591, 7879, 8011, 8389, 8539, 8599, 8629

Offset

1,1

Comments

Subsequence of A211656, A211660, and A211678.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

Prime 199 is in sequence because 197 and 199 are twin primes, sigma(197) = 198, sigma(199) = 200 and there are no other numbers m, n with sigma(m) = 198 or sigma(n) = 200.

Mathematica

d = DivisorSigma[1, Range[10000]]; t = Transpose[Select[Tally[Sort[d]], #[[2]] == 1 && #[[1]] <= Length[d] &]][[1]]; t2 = Sort[Flatten[Table[Position[d, i], {i, t}]]]; t3 = Select[t2, PrimeQ]; tp = {}; Do[If[t3[[i + 1]] - t3[[i]] == 2, AppendTo[tp, t3[[i + 1]]]], {i, Length[t3] - 1}]; tp (* T. D. Noe, Apr 26 2012 *)

Crossrefs

Cf. A211678 (twin primes p, p+2 with unique values of sigma(p) and sigma(p+2)), A211767 (lesser of twin primes p, p+2 with unique values of sigma(p) and sigma(p+2)).

Sequence in context: A123536 A057177 A297535 * A265031 A229030 A229033

Adjacent sequences: A211766 A211767 A211768 * A211770 A211771 A211772

Keyword

nonn

Author

Jaroslav Krizek, Apr 20 2012

Extensions

A-number corrected by Jaroslav Krizek, Mar 17 2013

Status

approved