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

0,2

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.

Links

Table of n, a(n) for n=0..50.

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).

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

Sequence in context: A124663 A101005 A029998 * A319670 A047005 A338513

Adjacent sequences: A117458 A117459 A117460 * A117462 A117463 A117464

Keyword

easy,nonn,base

Author

Enoch Haga, Mar 18 2006

Status

approved