A065913 Smallest prime of form (n+1)^k-n^k.

3, 5, 7, 61, 11, 13, 1273609, 17, 19, 331, 23, 6431804812640900941, 547, 29, 31, 371281, 919, 37, 723901, 41, 43

Offset: 1

Author

Labos Elemer, Nov 28 2001

Keywords

• nonn

Comments

Comments from Alexander Adamchuk, Dec 01 2006: (Start)

All odd primes appear in a(n) at least once. The first appearance of an odd prime p is at n = (p-1)/2.

a((p-1)/2) = p for an odd prime p.

a(22) = 23^229 - 22^229 is too large to include. It has 312 decimal digits.

a(23)-a(46) = {47, 1801, 1951, 53, 2269, 2437, 59, 61, 4925281, 3169, 67, 3571, 71, 73, 4219, 4447, 79, 30914273881, 83, 5419, 3679488080703419029992001830200360494989758810080014618823621, 89, 6211, 23382031}.

a(47) = 48^58543 - 47^58543 is too large to include. It has 98425 decimal digits.

a(48)-a(58) = {97, 7351, 101, 103, 8269, 107, 109, 9241, 113, 54664711, 10267}.

a(59) = 60^4663 - 59^4663. It has 8292 decimal digits.

a(60) = 61^54517 - 60^54517. It has 97331 decimal digits.

a(61)-a(81) = {713835580568173731369609539971, 11719, 127, 86548801, 131, 13267, 13669, 137, 139, 496940436849933148484939822444032113390611498072883923298539774627631945868169334995191, 113800495603976028899998661913482644451644387715995710215436605525039737336830571095980506932977448410777858266201, 58329802318048613482563140972219929, 2639948386755753473388124912433009743732807, 149, 151, 153322207649456947462552507840652437, 1517045588059, 157, 1767611013841, 19441, 163}.

a(82) = 83^331 - 82^331. It has 636 decimal digits.

a(83) = 167.

a(84) = 85^179 - 84^179. It has 346 decimal digits.

a(85)-a(105) = 267217051, 173, 293109961, 23497, 179, 181, 25117, 488904527834196204158742748944541, 26227, 2081544344660333015884252162151127102699920950101669675583052736376217501372173959207735927588562334550194111760450436831, 191, 193, 6014268846559, 197, 199, 53397779357967755570376892781394768316196882820228621180807406343608647492333350034301, 530707531, 17492708299776808914354631, 8605791381097, 596286601, 211. (End)

Links

• Ray Chandler, Table of n, a(n) for n = 1..46

Crossrefs

Cf. A058013

Formula

a(n) = (n+1)^A058013(n)-n^A058013(n)