A211767 Lesser 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.

3, 5, 197, 281, 347, 461, 641, 821, 857, 1289, 1697, 1721, 1787, 1877, 2081, 2141, 2381, 2549, 2801, 3257, 3539, 3557, 3929, 4019, 4241, 4637, 4721, 5441, 5477, 5501, 5657, 6449, 6689, 6701, 6761, 6827, 6947, 7457, 7589, 7877, 8009, 8387, 8537, 8597, 8627

Offset

1,1

Comments

Subsequence of A211656, A211660, A211678.

Links

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

Example

Prime 197 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]]]], {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)), A211769 (greater of twin primes p, p+2 with unique values of sigma(p) and sigma(p+2)).

Sequence in context: A337158 A333413 A104996 * A224537 A175133 A012817

Adjacent sequences: A211764 A211765 A211766 * A211768 A211769 A211770

Keyword

nonn

Author

Jaroslav Krizek, Apr 20 2012

Extensions

A-number corrected by Jaroslav Krizek, Mar 17 2013

Status

approved