(Translated by https://www.hiragana.jp/)
# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a007506 Showing 1-1 of 1 %I A007506 M1554 #79 Sep 08 2024 12:11:56 %S A007506 2,5,71,369119,415074643,55691042365834801 %N A007506 Primes p with property that p divides the sum of all primes <= p. %C A007506 a(6) > 29505444491. - _Jud McCranie_, Jul 08 2000 %C A007506 a(6) > 10^12. - _Jon E. Schoenfield_, Sep 11 2008 %C A007506 a(6), if it exists, is larger than 10^14. - _Giovanni Resta_, Jan 09 2014 %C A007506 Also primes p with property that p divides 1 plus the sum of all composites < p. - _Vicente Izquierdo Gomez_, Aug 05 2014 %C A007506 a(7) > 253814097223614463, - _Paul W. Dyson_, Sep 27 2022 %D A007506 J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 71, p. 25, Ellipses, Paris 2008. %D A007506 Harry L. Nelson, Prime Sums, J. Rec. Math., 14 (1981), 205-206. %D A007506 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). %D A007506 David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987. See p. 129. %H A007506 H. L. Nelson, Letter to the Editor re: Prime Sums, J. Recreational Mathematics 14.3 (1981-2), 205. (Annotated scanned copy) %H A007506 Carlos Rivera, Puzzle 18. Some special sums of consecutive primes, The Prime Puzzles and Problems Connection. %e A007506 2 divides 2; %e A007506 5 divides 2 + 3 + 5; %e A007506 71 divides 2 + 3 + 5 + 7 + ... + 61 + 67 + 71; etc. %t A007506 sumOfPrimes = 0; Do[ sumOfPrimes += p; If[ Divisible[ sumOfPrimes, p], Print[p]], {p, Prime /@ Range[23000000]}] (* _Jean-François Alcover_, Oct 22 2012 *) %t A007506 Transpose[Module[{nn=23000000,pr},pr=Prime[Range[nn]];Select[Thread[ {Accumulate[ pr], pr}], Divisible[#[[1]],#[[2]]]&]]][[2]] (* _Harvey P. Dale_, Feb 09 2013 *) %o A007506 (PARI) s=0;forprime(p=2,1e9,s+=p;if(s%p==0,print1(p", "))) \\ _Charles R Greathouse IV_, Jul 22 2013 %Y A007506 Cf. A024011, A028581, A028582. %K A007506 nonn,nice,hard,more %O A007506 1,1 %A A007506 _N. J. A. Sloane_, _Robert G. Wilson v_ %E A007506 Example corrected by _Harvey P. Dale_, Feb 09 2013 %E A007506 a(6) from _Paul W. Dyson_, Apr 16 2022 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE