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 A274995 a(n) is the smallest odd prime that divides (-n) + the sum of all smaller primes, or 0 if no such prime exists. 2
 5, 19, 3, 7, 82811, 3, 11, 17, 3, 191, 5, 3, 37, 29, 3, 5, 69431799799, 3, 1105589, 28463, 3, 431, 2947308589, 3, 7, 5, 3, 59, 11, 3, 5, 7, 3, 41 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS From Robert G. Wilson v, Nov 15 2016: (Start) If n == 2 (mod 3) then a(n) = 3; If n == 0 (mod 5) then a(n) = 5; If n == 3 (mod 7) then a(n) = 7; If n == 6 (mod 11) then a(n) = 11; If n == 2 (mod 13) then a(n) = 13; If n == 7 (mod 17) then a(n) = 17; If n == 1 (mod 19) then a(n) = 19; If n == 8 (mod 23) then a(n) = 23; in that order; i.e., from smaller to greater prime modulus, etc. First occurrence of p>2: 2, 0, 3, 6, 54, 7, 1, 123, 13, 36, 12, 33, 453, 46, ..., . (End) The congruence classes in the above list, modulo the prime bases, namely 2, 0, 3, 6, 2, ..., are given by A071089, in which each term is the remainder when the sum of the first n primes is divided by the n-th prime. - Neil Fernandez, Nov 23 2016 LINKS Robert G. Wilson v, n and a(n), or 0 if no such value is known, for n=0..10000 EXAMPLE a(1) = 19 because 19 is the smallest odd prime that divides the sum of (-1) + (sum of all primes smaller than itself), that is, -1 + 58 = 57. a(7) = 17 because -7 + 2 + 3 + 5 + 7 + 11 + 13 + 17 = 49 and 49/7 = 7. MATHEMATICA f[n_] := Block[{p = 3, s = 2 - n}, While[ Mod[s, p] != 0, s = s + p; p = NextPrime@ p]; p]; Array[f, 16, 0] (* Robert G. Wilson v, Nov 15 2016 *) PROG (PARI) sump(n) = s = 0; forprime(p=2, n-1, s+=p); s; a(n) = {my(p=3); while ((sump(p)-n) % p, p = nextprime(p+1)); p; } \\ Michel Marcus, Nov 12 2016 (PARI) a(n)=my(s=2); forprime(p=3, , if((s-n)%p==0, return(p)); s+=p) \\ Charles R Greathouse IV, Nov 15 2016 CROSSREFS Cf. A007504, A007506, A071089, A274649. Sequence in context: A342175 A258080 A318181 * A089082 A217011 A106229 Adjacent sequences:  A274992 A274993 A274994 * A274996 A274997 A274998 KEYWORD nonn,more AUTHOR Neil Fernandez, Nov 11 2016 EXTENSIONS a(16)-a(33) from Charles R Greathouse IV, Nov 15 2016 STATUS approved

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Last modified January 27 13:45 EST 2022. Contains 350607 sequences. (Running on oeis4.)