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A117461
Indices associated with primes in A117460. Both primes and their indices, after calculation of their respective digit sums, bear the relationship that both are prime and that sod(i) < sod(p) and sod(p) is the next prime after to sod(i), where sod is the sum of digits function.
3
1, 2, 3, 14, 30, 43, 74, 142, 184, 214, 238, 241, 256, 287, 292, 308, 313, 346, 443, 449, 472, 544, 593, 601, 607, 623, 715, 737, 791, 814, 836, 854, 874, 881, 883, 913, 931, 973, 980, 995, 1088, 1156, 1237, 1307, 1316, 1343, 1381, 1396, 1462, 1565, 1622
OFFSET
0,2
COMMENTS
A117458-A117459 is the opposite case where sod(i) > sod(p).
A117460-A117461 is sod(i) < sod(p).
A033548-A033549 is sod(i) = sod(p). - G. L. Honaker, Jr.
FORMULA
SOD's are calculated for these indices; if they and their associated prime SOD's are both prime and bear the relation in the Brief description above, they are added to the sequence.
EXAMPLE
a(4) = 30. Its associated prime is 113 with sod = 5; sod(a(4)) = 3. Since 3 < 5 and 5 is the next prime after 3, a(4) belongs in the sequence.
PROG
(UBASIC)
10 'use of str, mid, len, val
20 'in 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 and J=nxtprm(I) then stop
170 I=0:J=0
180 goto 40
CROSSREFS
Cf. A007953 (sum of digits).
Sequence in context: A124663 A101005 A029998 * A319670 A047005 A338513
KEYWORD
easy,nonn,base
AUTHOR
Enoch Haga, Mar 18 2006
STATUS
approved