The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.



Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A120811 Positive integers n such that n+d+1 is prime for all proper divisors d of n. Generalization of twin prime to all integers. 2
3, 5, 9, 11, 17, 27, 29, 35, 39, 41, 59, 65, 71, 101, 107, 125, 137, 149, 179, 191, 197, 227, 237, 239, 269, 281, 305, 311, 347, 417, 419, 431, 437, 461, 521, 569, 597, 599, 617, 641, 659, 671, 749, 755, 809, 821, 827, 857, 881, 905, 935, 989, 1019, 1031, 1049 (list; graph; refs; listen; history; text; internal format)



This sequence (A120811) is a generalization of twin prime (A001359), the sequence A120776 is a generalization of Sophie Germain prime (A005384), while A120806 is the generalization of Sophie germain twin prime (A045536). The same observations apply to A120811 as to A120806: the elements are (a) twin primes, (b) semiprimes pq, (c) 3-almost-primes, (d) 4-almost-primes. Moreover, the sequence includes all twin primes but in (b), (c) and (d) the containments are proper. The first occurrence of (d) is A120811(3980)=3^3*13147. Any others? A120811 CONJECTURE: These are all the elements, that is, no element of A120811 has more than 3 prime factors with no degree (sum of exponents) higher than 4.


T. D. Noe, Table of n, a(n) for n=1..1000


a(n)=n-th number such that n+d+1 is prime for all proper divisors d of n.


a(6)=27 since proper divisors={1,3,3^2} and 27+d+1={29,31,37} are all prime.

a(3980)=3^3*13147 since proper divisors={1,3,3^2,3^3,13147,3*13147,3^2*13147} and a(3980)+d+1={354971,354973,354979,354997,368117,394411,473293} are all prime.


with(numtheory); L:=[]: for w to 1 do for k from 1 while nops(L)<=5000 do x:=2*k+1; if isprime(x+2) then S:=divisors(x) minus {x}; Q:=map(z-> x+z+1, S); if andmap(isprime, Q) then fd:=fopen("C:/temp/n+d+1=prime-lower.txt", APPEND); fprintf(fd, "%d", x); fclose(fd); L:=[op(L), x]; print(nops(L), ifactor(x)); fi; #Q fi; #x od od;


Select[Range[2, 1100], AllTrue[#+Most[Divisors[#]]+1, PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 22 2020 *)


Cf. A120806, A120776, A120806, A001359, A005384, A045536.

Sequence in context: A302596 A230721 A094509 * A340287 A123069 A270836

Adjacent sequences:  A120808 A120809 A120810 * A120812 A120813 A120814




Walter Kehowski, Jul 07 2006



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 9 06:07 EST 2021. Contains 349627 sequences. (Running on oeis4.)