cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A120341 Sequence of pairs numerator(s(n)), denominator(s(n)) where s(n) is the n-th partial sum of 1/A119753(n).

Original entry on oeis.org

1, 3, 8, 15, 71, 105, 886, 1155, 12673, 15015, 255802, 285285, 18447227, 20255235, 1366902806, 1478632155, 109463953829, 116811940245, 15332301522476, 16236859694055, 6624458815881211, 6998086528137705, 2875388753804702068
Offset: 1

Views

Author

Walter Kehowski, Jun 23 2006

Keywords

Comments

There are only 66 terms of A119753 known and s(66) is 0.95578109643864566820083634846514203365246166270989 to 50 decimal places. What is sum(1/A119753(k),k=1..infinity)?

Examples

			a(5)=71, a(6)=105 since s(3)=1/3+1/5+1/7=71/105.

Crossrefs

Cf. A119751, A119753.

Formula

a(2n-1) = numerator(s(n)), a(2n)=denominator(s(n)), where s(n)=sum(1/A119753(k),k=1..n).

Extensions

This is not really a sequence. The standard OEIS convention would be to split this into two cross-referenced sequences with keyword "frac". - N. J. A. Sloane, Jul 22 2006

A120340 Sequence of pairs numerator(s(n)), denominator(s(n)) where s(n) is the n-th partial sum of 1/A119751(n).

Original entry on oeis.org

1, 1, 4, 3, 13, 9, 302, 207, 43255, 29601, 58966432, 40346163, 1700782246897, 1163704379409, 687683872186748, 470524470741039, 209415712651415308217, 143285523403473419397, 552462361711804327497414320
Offset: 1

Views

Author

Walter Kehowski, Jun 23 2006

Keywords

Comments

There are only 11 terms of A119751 known and s(11) is 1.4615274858438132136894180577690622581842692760227 to 50 decimal places. What is sum(1/A119751(k),k=1..infinity)?

Examples

			a(5)=13, a(6)=9 since s(3)=1+1/3+1/9=13/9.

Crossrefs

Cf. A119751, A119753.

Formula

a(2n-1) = numerator(s(n)), a(2n)=denominator(s(n)), where s(n)=sum(1/A119751(k),k=1..n).

Extensions

This is not really a sequence. The standard OEIS convention would be to split this into two cross-referenced sequences with keyword "frac". - N. J. A. Sloane, Jul 22 2006

A120402 a(1)=2; a(n)=first even number greater than a(n-1) such that 2*a(n)-1 is prime and a(i)+a(n)-1 is prime for all 1<=i<=n-1.

Original entry on oeis.org

2, 4, 10, 70, 430, 4090, 86530, 513100, 913570, 7914340, 6593621380, 9366241600
Offset: 1

Views

Author

Walter Kehowski, Jul 02 2006

Keywords

Comments

All elements after the first are 4 mod 6. In base 12 the sequence is 2, 4, X, 5X, 2EX, 244X, 420XX, 208E24, 38082X, 2798084, where X is 10 and E is eleven.

Examples

			a(2)=4 since 4 is the first even number > a(1)=2 such that 2*4-1=7 is prime and 4+2-1=5 is prime.

Crossrefs

Cf. A119752, A119754, A119751, A119753, A103828.

Programs

  • Maple
    EP:=[2]: for w to 1 do for k from 0 to 12^8 do n:=6*k+4; p:=2*n-1; Q:=map(z-> z+n-1, EP); if isprime(p) and andmap(isprime,Q) then EP:=[op(EP),n]; print(n); fi od od;

Formula

a(1)=2; a(n) = s where s is the first even number s>a(n-1) such that 2*s-1 is prime and s+a(i)-1 is prime, 1<=i<=n-1.

Extensions

a(11)-a(12) from Bert Dobbelaere, Apr 17 2019

A120403 a(1)=3; a(n)=first odd number greater than a(n-1) such that 2*a(n)-1 is prime and a(i)+a(n)-1 is prime for all 1<=i<=n-1.

Original entry on oeis.org

3, 9, 15, 45, 225, 639, 1275, 4005, 675405, 2203959, 3075159, 6195234165, 77989711185, 4566262987329
Offset: 1

Views

Author

Walter Kehowski, Jul 02 2006

Keywords

Comments

All elements are 3 mod 6. In base 12 the sequence is 3, 9, 13, 39, 169, 453, 8X3, 2399, 286X39, 8X3533, 1043733, where X is 10 and E is eleven.

Examples

			a(2)=9 since 9 is the first odd number > a(1)=3 such that 2*9-1=17 is prime and 9+3-1=13 is prime.

Crossrefs

Cf. A119752, A119754 (resulting primes), A119751, A119753, A103828.

Programs

  • Maple
    OP:=[3]: for w to 1 do for k from 0 to 12^8 do n:=6*k+3; p:=2*n-1; Q:=map(z-> z+n-1, OP); if isprime(p) and andmap(isprime,Q) then OP:=[op(OP), n]; print(n); fi od od;

Formula

a(1)=3; a(n) = s where s is the first odd number s>a(n-1) such that 2*s-1 is prime and s+a(i)-1 is prime, 1<=i<=n-1.
a(n) = A119752(n) + 1. - Chandler

Extensions

a(12)-a(14) from Ray Chandler, Apr 04 2010
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.