A169645 Primes p = prime(k) whose decimal expansion contains the string 13 and such that digsum(p) = disgum(k) where digsum = A007953 is the sum of digits function.

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

Links

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

Example

131 = prime(32), r = 1, digsum(k) = 5.
1913 = prime(293), s = 19, digsum(k) = 14.
3137 = prime(446), t = 3, u = 7, digsum(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. A166573, A175017

Subsequence of A033548.

Sequence in context: A142807 A103834 A281393 * A221154 A144247 A161197

Adjacent sequences: A169642 A169643 A169644 * A169646 A169647 A169648

Keyword

base,less,nonn

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

Revised by Sean A. Irvine, Feb 20 2026

Status

approved