The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A144062

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A144062

a(1)=1; for n>1, a(n) = least integer > a(n-1) such that a(n)^2-a(n-1)^2 = semiprime
(history; published version)

#10 by Harvey P. Dale at Tue Oct 18 09:36:32 EDT 2016

STATUS

editing

approved

#9 by Harvey P. Dale at Tue Oct 18 09:36:28 EDT 2016

LINKS

Harvey P. Dale, <a href="/A144062/b144062.txt">Table of n, a(n) for n = 1..1000</a>

MATHEMATICA

sp[n_]:=Module[{k=n+1}, While[PrimeOmega[k^2-n^2]!=2, k++]; k]; NestList[ sp, 1, 60] (* Harvey P. Dale, Oct 18 2016 *)

STATUS

approved

editing

#8 by Bruno Berselli at Fri Feb 28 09:00:12 EST 2014

STATUS

proposed

approved

#7 by Michel Marcus at Fri Feb 28 08:57:16 EST 2014

STATUS

editing

proposed

#6 by Michel Marcus at Fri Feb 28 08:55:24 EST 2014

DATA

1, 4, 5, 8, 11, 18, 23, 30, 37, 42, 43, 44, 57, 58, 69, 80, 81, 86, 93, 94, 97, 100, 101, 102, 103, 108, 109, 110, 111, 116, 123, 124, 125, 132, 133, 134, 137, 140, 143, 144, 145, 146, 165, 172, 175, 178, 181, 186, 193, 196, 197, 198, 203, 204, 215, 218, 219

PROG

(PARI) lista(nn) = {cura = 1; print1(cura, ", "); for (n=1, nn, nexta = cura + 1; while (bigomega(nexta^2-cura^2) != 2, nexta++); cura = nexta; print1(nexta, ", "); ); } \\ Michel Marcus, Feb 28 2014

CROSSREFS

Cf. A001358.

EXTENSIONS

Corrected and extended by Michel Marcus, Feb 28 2014

STATUS

approved

editing

Discussion

Fri Feb 28

08:57

Michel Marcus: Terms added 94 and 140.
94^2-93^2=187=11*17 and 140^2-137^2=831=3*277

#5 by Bruno Berselli at Mon Jan 21 09:59:25 EST 2013

STATUS

reviewed

approved

#4 by Jean-François Alcover at Mon Jan 21 09:39:35 EST 2013

STATUS

proposed

reviewed

#3 by Michel Marcus at Mon Jan 21 09:38:28 EST 2013

STATUS

editing

proposed

#2 by Michel Marcus at Mon Jan 21 09:38:23 EST 2013

NAME

a(1)=1; for n>&, 1, a(n) = least integer > a(n-1) such as that a(n)^2-a(n-1)^2 = semiprime

EXAMPLE

2^2-1=3, not semiprime ; 3^2-1=8; , not semiprime ; 4^2-1=15=3*5= , semiprime, hence a(2)=4.

STATUS

approved

editing

#1 by N. J. A. Sloane at Fri Jan 09 03:00:00 EST 2009

NAME

a(1)=1; for n>&, a(n) = least integer > a(n-1) such as a(n)^2-a(n-1)^2 = semiprime

DATA

1, 4, 5, 8, 11, 18, 23, 30, 37, 42, 43, 44, 57, 58, 69, 80, 81, 86, 93, 97, 100, 101, 102, 103, 108, 109, 110, 111, 116, 123, 124, 125, 132, 133, 134, 137, 143, 144, 145, 146

OFFSET

1,2

EXAMPLE

2^2-1=3, not semiprime 3^2-1=8; not semiprime 4^2-1=15=3*5= semiprime, hence a(2)=4

KEYWORD

easy,nonn

AUTHOR

Philippe Lallouet (philip.lallouet(AT)orange.fr), Sep 09 2008

STATUS

approved