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 A129469 Least prime of Erdos-Selfridge class n+ in A129470. 9
 883, 3181, 15913, 2146141, 17227801, 456185017, 4960846573, 568124640697, 2273325467773, 145351829612377, 9302101084613641, 595332797734595317, 5813792718345189961, 1139502378775815768313, 166245781044286357673761 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,1 COMMENTS The sequence starts at offset 3, since primes of class 1+ and 2+ have all prime factors (of p+1) of class 1+. Definitions imply that a(n) >= -1+2*A005113(n-1)*nextprime(1+A005113(n-1)). We have a(n) = -1+2*A005113(n-1)*p for all n<18, with p prime for n>3. This holds probably for all n. LINKS EXAMPLE a(3) = 883 = -1+2*13*17 is a prime of class 3+ since 13 is of class 2+, but the largest divisor of 883+1 is 17 which is only of class 2+. a(4) = 3181 = -1+2*37*43 is a prime of class 4+ since 37 is of class 3+, but the largest divisor of 3181+1 is 43 which is only of class 2+. PROG (PARI) class(n, s=1)={n=factor(n+s)[, 1]; if(n[ #n]<=3, 1, for(i=2, #n, n=max(class(n[i], s)+1, n)); n)}; A129469={vector(#A005113-1, i, t=A005113[i+1]; t=[t, nextprime(t+1)-1, 0]; until( isprime( t = -1+2*t*t ) & (f=factor( 1+t )[, 1]) & class(f[ #f], 1)= i+1, print("Warning, crossed a prime of class >= ", i+1, "+, p=", t); ); ); print(i+2, " ", t); t)} CROSSREFS Cf. A129470, A005113, A005105 - A005108, A081633 - A081639, A084071, A090468, A129474 - A129475. Sequence in context: A129470 A129471 A023312 * A206794 A206964 A209089 Adjacent sequences:  A129466 A129467 A129468 * A129470 A129471 A129472 KEYWORD nonn AUTHOR M. F. Hasler, Apr 16 2007 STATUS approved

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Last modified August 10 20:21 EDT 2022. Contains 356039 sequences. (Running on oeis4.)