A169645 Primes p = prime(k) of form 13//r, s//13 or t//13//u and sod(p) = sod(k).

131, 1301, 1361, 1913, 3137, 7013, 7213, 11353, 12613, 13007, 13037, 13127, 13217, 13297, 13327, 13339, 13367, 13417, 13457, 13933, 15913, 18013, 22613, 29131, 31391, 41131, 41333, 51131, 54013, 57139, 57713, 63313, 64513, 65713, 68813, 70139, 71353, 74713

Offset

1,1

Comments

Sum of digits of p = prime(k), p containing the string "13", equals sum of digits of the prime index k

A subsequence of A033548

Still no (published) proof if sequence is infinite

Links

Table of n, a(n) for n=1..38.

Example

13//1 = 131 = prime(32), r = 1, sod(k) = 5
19//13 = 1913 = prime(293), s = 19, sod(k) = 14
3//13//7 = 3137 = prime(446), t = 3, u = 7, sod(k) = 14

Mathematica

sodQ[{a_, b_}]:=SequenceCount[IntegerDigits[b], {1, 3}]>0&&Total[ IntegerDigits[ a]] ==Total[IntegerDigits[b]]; Select[Table[ {n, Prime[n]}, {n, 7000}], sodQ][[All, 2]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 10 2018 *)

Crossrefs

Cf. A033548, A166573, A175017

Sequence in context: A142807 A103834 A281393 * A221154 A144247 A161197

Adjacent sequences: A169642 A169643 A169644 * A169646 A169647 A169648

Keyword

base,nonn,uned

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Apr 05 2010

Extensions

Corrected and extended by Harvey P. Dale, May 10 2018

Status

approved