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

Author

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

Keywords

• base
• nonn
• uned

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

Examples

			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
		

Crossrefs

Cf. A033548, A166573, A175017

Programs

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 *)

Extensions

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