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 A247246 Differences of consecutive Achilles numbers. 1
 36, 92, 88, 104, 40, 68, 148, 27, 125, 64, 104, 4, 153, 27, 171, 29, 20, 196, 232, 144, 56, 312, 280, 108, 188, 199, 113, 67, 189, 72, 344, 16, 112, 232, 268, 63, 45, 392, 292, 32, 76, 8, 80, 587, 50, 147, 456, 184, 288, 488, 115, 772, 137, 36, 40, 212, 248 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 29 is the first prime in this sequence, and it equals 1352 - 1323. Clearly, if the difference is prime, then these two Achilles numbers must be relatively prime, so primes appear in this sequence rarely. However, are there infinitely many n such that a(n) is prime? The number 1 can also appear in this sequence, because it equals 5425069448 - 5425069447 = (2^3 * 26041^2) - (7^3 * 41^2 * 97^2). Does every natural number appear in this sequence? If so, do they appear infinitely often? LINKS Carlos Rivera, Problem 53 Eric Weisstein's World of Mathematics, Achilles number Wikipedia, Achilles number FORMULA a(n) = A052486(n+1) - A052486(n). MAPLE f:= proc(n) local E; E:= map(t->t[2], ifactors(n)[2]); min(E)>1 and igcd(op(E))=1 end proc: Achilles:= select(f, [\$1..10^5]): seq(Achilles[i+1]-Achilles[i], i=1..nops(Achilles)-1); # Robert Israel, Dec 13 2014 PROG (PARI) isA052486(n) = { n>1 & vecmin(factor(n)[, 2])>1 & !ispower(n); } lista(nn) = {v = select(n->isA052486(n), vector(nn, i, i)); vector(#v-1, n, v[n+1] - v[n]); } \\ Michel Marcus, Nov 29 2014 CROSSREFS Cf. A052486, A076446, A053289. Sequence in context: A305068 A182467 A060936 * A242238 A200866 A324297 Adjacent sequences:  A247243 A247244 A247245 * A247247 A247248 A247249 KEYWORD nonn,easy AUTHOR Eric Chen, Nov 28 2014 STATUS approved

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Last modified June 2 18:17 EDT 2020. Contains 334787 sequences. (Running on oeis4.)