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A117477
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Primes whose SOD and that of their indices are both prime and equal (indices may not be prime, but their SOD must be prime).
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1
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131, 263, 1039, 1091, 1301, 1361, 1433, 2221, 2441, 2591, 2663, 2719, 2803, 3433, 3631, 4153, 4357, 4397, 5507, 5701, 5741, 5927, 6311, 6353, 6553, 6737, 6827, 6971, 7013, 7213, 7411, 7523, 7741, 8821, 9103, 11173, 11353, 11731, 11821, 12277, 12347
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refs;
listen;
history;
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internal format)
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OFFSET
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1,1
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COMMENTS
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"SOD" = "sum of digits".
This sequence is a subset of A033548, the difference being that this sequence requires prime SODs.
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LINKS
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FORMULA
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Find primes whose indices, when SODs are computed, are both prime and SOD(i) = SOD(p)
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EXAMPLE
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a(3) = 1039, the 175th prime. Both the SOD of the index and the prime are prime and equal: 13 = 13.
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MATHEMATICA
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sodQ[{n_, p_}]:=Module[{sodn=Total[IntegerDigits[n]], sodp=Total[IntegerDigits[p]]}, AllTrue[ {sodn, sodp}, PrimeQ] && sodn == sodp]; Select[With[{nn=1500}, Table[{n, Prime[n]}, {n, nn}]], sodQ][[;; , 2]] (* Harvey P. Dale, Apr 20 2024 *)
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PROG
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(UBASIC)
20 'SOD prime index and SOD prime
30 Y=1
40 Y=nxtprm(Y)
50 C=C+1:print C; Y; "-";
60 D=str(C):Z=str(Y)
70 E=len(D):F=len(Z)
80 for Q=2 to E
90 A=mid(D, Q, 1):G=val(A)
100 I=I+G:print I;
110 next Q
120 for R=2 to F
130 B=mid(Z, R, 1):H=val(B)
140 J=J+H:print J;
150 next R
160 if I=prmdiv(I) and J=prmdiv(J) and I=J then stop
170 I=0:J=0
180 goto 40
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CROSSREFS
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KEYWORD
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easy,nonn,base,changed
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AUTHOR
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STATUS
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approved
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