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 A121091 Smallest nexus prime of the form n^p - (n-1)^p, where p is an odd prime. 3
 7, 19, 37, 61, 4651, 127, 1273609, 2685817, 271, 331, 397, 6431804812640900941, 547, 631, 5613125740675652943160572913465695837595324940170321, 371281, 919 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS a(19) = 19^1607 - 18^1607, which is too large to include. It has 2055 decimal digits. See A062585(1) = 1607. a(20)-a(21) = {723901, 8005616640331026125580781}. a(n) is currently known for all n up to n = 96. Corresponding smallest odd primes p such that (n+1)^p - n^p is prime are listed in A125713(n) = {3,3,3,3,5,3,7,7,3,3,3,17,3,3,43,5,3,10957,5,19,127,229,3,3,3,13,3,3,149,3,5,3,23,3,5,83,3,3,37,7,3,3,37,5,3,5,58543,...}. a(n+1) = A065013(n) for n = {4, 7, 10, 12, 13, 16, 17, 19, 22, 24, 25, 27, 28, 31, ...} = A047845(n) = (n-1)/2, where n runs through odd nonprimes (A014076), for n>1. LINKS FORMULA a(n) = n^A125713(n) - (n-1)^A125713(n). CROSSREFS Cf. A121620, A000043, A058765, A121616, A121618. Cf. A125713 = Smallest odd prime p such that (n+1)^p - n^p is prime. Cf. A065913 = Smallest prime of form (n+1)^k - n^k. Cf. A058013 = Smallest prime p such that (n+1)^p - n^p is prime. Cf. A047845, A014076. Cf. A062585 = numbers n such that k^n - (k-1)^n is prime, where k is 19. Cf. A000043, A057468, A059801, A059802, A062572-A062666. Sequence in context: A155361 A155315 A155323 * A213489 A288021 A155394 Adjacent sequences: A121088 A121089 A121090 * A121092 A121093 A121094 KEYWORD nonn AUTHOR Alexander Adamchuk, Aug 11 2006, revised Dec 01 2006, Feb 15 2007 STATUS approved

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Last modified March 26 11:46 EDT 2023. Contains 361549 sequences. (Running on oeis4.)