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A169645
Primes p = prime(k) of form 13//r, s//13 or t//13//u and sod(p) = sod(k).
0
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
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
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