A117460 Primes prime(i) such that their sum-of-index-digits A007953(i) and their sum-of-digits A007605(i) are consecutive primes.

2, 3, 5, 43, 113, 191, 373, 821, 1097, 1307, 1493, 1523, 1619, 1873, 1907, 2029, 2081, 2339, 3109, 3169, 3347, 3923, 4339, 4421, 4463, 4603, 5417, 5581, 6067, 6263, 6427, 6607, 6791, 6841, 6863, 7127, 7307, 7673, 7723, 7877, 8731, 9341, 10079, 10723

Offset

1,1

Comments

We select primes such that their sum-of-digits is some prime(j) and such that in addition the sum-of-digits of their index is prime(j-1).

Line 160 of the UBASIC program can be altered for <, >, or = relationships

Subset of A046704 - R. J. Mathar, Apr 17 2009

Links

Table of n, a(n) for n=1..44.

Formula

{A000040(i): A007605(i) = A000040(j) and A007953(i) = A000040(j+1) for some j}. - R. J. Mathar, Apr 17 2009

Example

"SOD" = "sum of digits": a(5) = 113, the prime whose index is 30. SOD(30) = 3 and SOD(113) = 5. Since 3 < 5 and 5 is nextprime to 3, adjoin 113 to 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 I=nxtprm(J) then stop 170 I=0:J=0 180 goto 40

Crossrefs

Cf. A117461, A117458, A117459, A033548, A033549.

Sequence in context: A362957 A042469 A107990 * A281252 A208223 A136371

Adjacent sequences: A117457 A117458 A117459 * A117461 A117462 A117463

Keyword

easy,nonn,base

Author

Enoch Haga, Mar 18 2006

Extensions

Edited by R. J. Mathar, Apr 17 2009

Status

approved