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.

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

Author

Enoch Haga, Mar 18 2006

Keywords

• easy
• nonn
• base

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.

Examples

			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.
		

Crossrefs

Cf. A007953 (sum of digits).

Cf. A117460, A117458, A117459, A033548, A033549.

Programs

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
				

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.