A241897 Primes p equal to the sum in base 3 of the digits of all primes < p - digit-sum of the index of prime p(i-1).

67, 71, 97, 101, 149, 223, 656267, 697511, 697951, 698447, 699493, 700277, 715373, 883963, 888203, 888211, 992021, 992183, 992891, 993241, 994181, 1155607, 1155829, 1308121, 1308649, 1310093, 1313083, 1317409, 1320061, 1320157, 1320379, 1322521, 1322591

Offset: 1

Author

Anthony Sand, May 01 2014

Keywords

• nonn
• base

Comments

There are no further solutions beyond a(46)=4539541 up to at least 10^10. - Andrew Howroyd, Mar 02 2018

Examples

			67 = digit-sum(2..61,b=3) - digit-sum(index(61),b=3) = sum(2) + sum(1,0) + sum(1,2) + sum(2,1) + sum(1,0,2) + sum(1,1,1) + sum(1,2,2) + sum(2,0,1) + sum(2,1,2) + sum(1,0,0,2) + sum(1,0,1,1) + sum(1,1,0,1) + sum(1,1,1,2) + sum(1,1,2,1) + sum(1,2,0,2) + sum(1,2,2,2) + sum(2,0,1,2) + sum(2,0,2,1) - digit-sum(200).
		

Links

• Anthony Sand, Table of n, a(n) for n = 1..46

Crossrefs

A240886. Primes p equal to the digit-sum in base 3 of all primes < p. A168161. Primes p which are equal to the sum of the binary digits in all primes <= p.

Programs

PARI

seq(maxp)={my(p=1,L=List(),s=0,k=0); while(pAndrew Howroyd, Mar 01 2018

Formula

prime(n) such that, using base 3, prime(n) = sum_{1..n-1} A239619(i) - sum_{index(n-1)}

Extensions

a(29)-a(33) from Andrew Howroyd, Mar 02 2018