1,2

All primes of the form 11...1 are in the sequence because if p=11...1 is a prime then sigma(p)+phi(p)+p=3p=33...3 is a repdigit number, so (10^A004023-1)/9 is a subsequence of this sequence. 37 is the only multi-digit prime term of the sequence which isn't of the form 11...1 - the proof is easy. Next term is greater than 2.3*10^10. - Farideh Firoozbakht (mymontain(AT)yahoo.com), Aug 24 2006

Also we have the following two assertions. - Farideh Firoozbakht (mymontain(AT)yahoo.com), Aug 24 2006

(a). If p=(2*10^(3n+2)-11)/27 is prime then m=2p is in the sequence because sigma(m)+phi(m)+m=6p+2=4*(10^(3n+2)-1)/9 is a repdigit number. 2*(2*10^29-11)/27 (a 29-digit number)is the smallest such terms of the sequence and the next such term(if it exists) has more than 20000 digits. - Farideh Firoozbakht (mymontain(AT)yahoo.com), Aug 24 2006

(b). If p=(4*10^(3n+1)-13)/27 is prime then m=2p is in the sequence because sigma(m)+phi(m)+m=8*(10^(3n+1)-1)/9 is a repdigit number. 2962 is the smallest such terms of the sequence. - Farideh Firoozbakht (mymontain(AT)yahoo.com), Aug 24 2006

3652175 + sigma(3652175) + phi(652175) = 11111111.

Cf. A116019.

Cf. A004023.

Sequence in context: A035122 A085305 A116032 this_sequence A060812 A062936 A136972

Adjacent sequences: A116026 A116027 A116028 this_sequence A116030 A116031 A116032

nonn,base

Giovanni Resta (g.resta(AT)iit.cnr.it), Feb 13 2006

More terms from Farideh Firoozbakht (mymontain(AT)yahoo.com), Aug 24 2006